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class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> AHL Static fluids <a href="#" class="mark-page-favorite pull-right" data-pid="1250" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../849/engineering.html">Engineering</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">AHL Static fluids</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 45 minutes"><i class="fa fa-clock-o"></i> 45'</span> </ol> <article id="main-article"> <p><img alt="" src="../../ahl-engineering/underwater-2615376_640.jpg" style="float: left; width: 250px; height: 141px;">Don't be fooled into thinking that only solids are 'heavy' and that we can approximate everything as a volume-less particle. Fluids, such as liquids, have a density, exert an upward buoyancy on anything that should displace them, have increasing pressure with depth and are used in hydraulics to exert huge forces.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Density</p> </div> </div> <div class="panel-body"> <div> <p>Density is a material property (like <a href="../190/resistivity.html" title="Resistivity">Resistivity</a>), which means that it is a constant value for a given material irrespective of its dimensions. The density of copper wire is the same as the density of a copper block.</p> <p>Density is defined as the ratio of the mass of an object to its volume:</p> <p style="text-align: center;"><span class="math-tex">\(\rho={m\over V}\)</span></p> <ul> <li><span class="math-tex">\(\rho\)</span> is density (kg m<sup>-3</sup>)</li> <li><span class="math-tex">\(m\)</span> is mass (kg)</li> <li><span class="math-tex">\(V\)</span> is volume (m<sup>-3</sup>)</li> </ul> <p>Solids (especially metals) have a high density due to their high concentration of particles; copper's density is approximately 9000 kg m<sup>-3</sup>. Liquids come next; water has a density of 1000 kg m<sup>-3</sup>. Gases have a low density; air has a density of approximately 1 kg m<sup>-3</sup> at sea level.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Buoyancy</p> </div> </div> <div class="panel-body"> <div> <p>Every object that displaces a fluid experiences the upward force of buoyancy as a consequence. For solid objects falling in the atmosphere, this is often negligible in comparison with upward drag forces. However, buoyancy can cause objects to float - provided that the density of the fluid matches or exceeds the density of the object.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Pressure</p> </div> </div> <div class="panel-body"> <div> <h4>At a surface</h4> <p>Pressure is the ratio of force acting to the surface area:</p> <p style="text-align: center;"><span class="math-tex">\(P={F\over A}\)</span></p> <ul> <li><span class="math-tex">\(P\)</span> is pressure (Pa)</li> <li><span class="math-tex">\(F\)</span> is force (N)</li> <li><span class="math-tex">\(A\)</span> is surface area (m<sup>2</sup>)</li> </ul> <ul> </ul> <h4>At a depth</h4> <p>It can be helpful to think of our lives as taking place at the bottom of an ocean of atmosphere. The atmosphere presses down on us due to gravity. While we do not feel impeded by this, atmospheric pressure has a value of approximately 10<sup>5</sup> Pa.</p> <p>Within a container of fluid, pressure increases with depth. This is because, the further down you go, the larger the force acting from the fluid above. Consider the force as emerging from the mass of the fluid, which in turn can be calculated using its density and volume. For a container of constant cross-sectional area:</p> <p style="text-align: center;"><span class="math-tex">\(P={F\over A}={m_f g\over A}={\rho_f V g\over A}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow P_f=\rho_f gd\)</span></p> <ul> <li><span class="math-tex">\(P_f\)</span> is the pressure in a fluid (Pa)</li> <li><span class="math-tex">\(\rho_f\)</span> is the density of the fluid (kg m<sup>-3</sup>)</li> <li><span class="math-tex">\(g\)</span> is gravitational field strength (on earth, 9.81 N kg<sup>-1</sup>)</li> <li><span class="math-tex">\(d\)</span> is depth (NB: downward from the surface) (m)</li> </ul> <p style="text-align: center;"><img alt="" src="../../ahl-engineering/800px-torricellilawdiagram.svg.png" style="width: 400px; height: 286px;"></p> <h6 style="text-align: center;">By Matt Cook - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=45705236</h6> <p>To find the total pressure acting at a depth in a fluid, we combine atomospheric pressure and the pressure due to the fluid:</p> <p style="text-align: center;"><span class="math-tex">\(P=P_0 +\rho_f gd\)</span></p> <ul> <li><span class="math-tex">\(P\)</span> is total pressure (Pa)</li> <li><span class="math-tex">\(P_0\)</span> is atmospheric pressure (on earth, 10<sup>5</sup> Pa)</li> <li><span class="math-tex">\(\rho_f\)</span> is the density of the fluid (kg m<sup>-3</sup>)</li> <li><span class="math-tex">\(g\)</span> is gravitational field strength (on earth, 9.81 N kg<sup>-1</sup>)</li> <li><span class="math-tex">\(d\)</span> is depth (NB: downward from the surface) (m)</li> </ul> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/388883236"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p> </p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Archimedes' principle</p> </div> </div> <div class="panel-body"> <div> <p>Archimedes' principle allows us to calculate the magnitude of fhe force of buoyancy. Buoyancy is equal to the weight of the fluid displaced, which we calculate using the fluid's density and volume (rather than mass):</p> <p style="text-align: center;"><span class="math-tex">\(B=\rho_f V_f g\)</span></p> <ul> <li><span class="math-tex">\(B\)</span> is buoyancy (N)</li> <li><span class="math-tex">\(\rho_f\)</span> is the density of the fluid (kg)</li> <li><span class="math-tex">\(V_f\)</span> is the volume of fluid that is displaced by the object (m<sup>3</sup>)</li> <li><span class="math-tex">\(g\)</span> is gravitational field strength (on earth, 9.81 N kg<sup>-1</sup>)</li> </ul> <p>For an object that is fully submerged, the volume of the displaced fluid is equal to the volume of the object. For a floating object or an object that is partly submerged, only the volume of the object withn the fluid displaces fluid. Note that it is impossible for an object to float without displacing any fluid (however much polystyrene might appear to rest on top of a container of water!).</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/388882832"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Pascal's principle</p> </div> </div> <div class="panel-body"> <div> <p>Pascal’s principle states that a change in pressure at any point in a confined fluid at rest is transmitted to all points in the fluid. For an incompressible fluid confined by two pistons, a change in pressure on the first piston causes an equal change in pressure on the second piston.</p> <p>We can calculate these pressures using combinations of the following equation for the change in pressure:</p> <p style="text-align: center;"><span class="math-tex">\(\Delta P={\Delta F \over A}=\rho_f g \Delta d\)</span></p> <ul> <li><span class="math-tex">\(\Delta P\)</span> is the change in pressure (Pa)</li> <li><span class="math-tex">\(\Delta F\)</span> is the change in force (N)</li> <li><span class="math-tex">\(A\)</span> is the cross-sectional area of a piston (m<sup>2</sup>)</li> <li><span class="math-tex">\(\rho_f\)</span> is the density of the fluid (kg m<sup>-3</sup>)</li> <li><span class="math-tex">\(g\)</span> is gravitational field strength (on earth, 9.81 N kg<sup>-1</sup>)</li> <li><span class="math-tex">\(\Delta d\)</span> is the compression or retraction distance moved through by a piston (m)</li> </ul> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/388879948"></iframe></div> <p>One implication of Pascal's principle is the ability of a single human to raise the height of a much heavier object. Provided the area of the piston below the heavy object is much larger than the area of the piston where the human force is exerted, the human force can be much smaller:</p> <p style="text-align: center;"><span class="math-tex">\({\Delta F_1\over A_1}={\Delta F_2\over A_2}\)</span></p> <p style="text-align: center;"><img alt="" src="../../ahl-engineering/working_principle_of_a_hydraulic_jack.svg" style="width: 300px; height: 178px;"></p> <p>This is an example of hydraulics, the use of fluids in engineering.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Hydrostatic equilibrium</p> </div> </div> <div class="panel-body"> <div> <p>A fluid is in hydrostatic equilibrium when it is at rest or when velocity is constant.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/388879959"></iframe></div> <h4>Measuring pressure: manometer</h4> <p>A manometer is a device for measuring the pressure acting on a fluid. It consists of a U-shaped tube with constant cross-sectional area containing a fluid.</p> <p>The pressure acting exerts a force on one side of the manometer tube. The fluid moves around the tube until hydrostatic equilibrium is reached. At this point, the relative heights of the fluid can be used to calculate the pressure.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/388879920"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>The ideal fluid</p> </div> </div> <div class="panel-body"> <div> <p>An ideal fluid is:</p> <ol> <li>Incompressible - density is constant no matter what pressure is exerted</li> <li>Nonviscous - there are no frictional forces between layers of fluid</li> <li>In steady flow - mass flowrate (the quantity of mass of a fluid moving past any point in a given quantity of time) is constant</li> </ol> <p>Ideal fluids do not exist, but we have used assumption '1' on this page. We will consider the others in the next section.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><em>Use flashcards to practise your recall.</em></p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="3" data-mode="Normal" data-topics="1032" data-subject-id="6" data-n-flashcards="19" style="text-align:center">Show flashcards</a></div><hr> <p><em>Use quizzes to practise application of theory.</em></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#e23c1ea0"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="e23c1ea0"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> AHL Static fluids <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-383-1250" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>1000 kg of water is contained in a 1 m<sup>3</sup> rigid cube. The cube and contents are falling freely close to the Earth. Atmospheric pressure is 100 kPa.</p><p style="text-align: center;"><img alt="" height="259" src="../../screenshot-2019-12-19-at-13.23.54.png" width="220"></p><p>The pressure exerted by the fluid on the bottom of the box is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>110 kPa</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>0 Pa</span></label> </p><p><label class="radio"> <input type="radio"> <span>10 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>100 kPa</span></label></p></div><div class="q-explanation"><p>Free-fall is equivalent to zero gravity so there is no pressure due to depth.</p><p>The container is rigid and contains no air so no there is pressure due to the atmosphere.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>1000 kg of water is contained in a 1 m<sup>3</sup> rigid cube by a frictionless piston. The cube and contents are falling freely close to the Earth. Atmospheric pressure is 100 kPa.</p><p style="text-align: center;"><img alt="" height="217" src="../../screenshot-2019-12-19-at-13.42.14.png" width="174"></p><p>The pressure exerted by the fluid on the bottom of the box is:</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>100 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>110 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>0 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>10 kPa</span></label> </p></div><div class="q-explanation"><p>Free-fall is equivalent to zero gravity so there is no pressure due to depth.</p><p>Atmospheric pressure acts on the piston. Since the piston is frictionless, the entirety of this atmospheric pressure acts on the fluid and is transmitted everywhere in the fluid.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>1000 kg of water is contained in a 1 m<sup>3</sup> rigid cube by a frictionless piston of mass 100 kg. The cube and contents are resting on the Earth. Atmospheric pressure is 100 kPa.</p><p style="text-align: center;"><img alt="" height="238" src="../../screenshot-2019-12-19-at-13.49.43.png" width="245"></p><p>The pressure exerted by the fluid on the bottom of the box is:</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>111 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>110 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>100 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>120 kPa</span></label> </p></div><div class="q-explanation"><p>The total pressure is the combination of atmosopheric pressure, the pressure due to depth and the pressure due to the piston:</p><p><span class="math-tex">\(P = P_0 + P_f + P_\text{piston} = 10^5 + 1000\times 10\times 1+{100\times 10\over 1}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A diver measures the pressure in a lake at 50 m and 100 m. The ratio <span class="math-tex">\(P_{50}\over P_{100}\)</span> is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(6\over 10\)</span></span></label></p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(6\over11\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(3\over 4\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(1\over 2\)</span></span></label></p></div><div class="q-explanation"><p>The trick is to remember to add atmospheric pressure. Atmospheric pressure is equivalent to the pressure at a depth of 10 m.</p><p>Since pressure at depth is proportional to depth for constant density and gravitational field strength:<span class="math-tex">\({P_{50}\over P_{100}}={50+10\over 100+10}={6\over 11}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A 10 m deep swimming pool is constructed on the Moon. What is the ratio <span class="math-tex">\(\text{pressure at the bottom of the Moon pool}\over \text{pressure at the bottom of an identical pool on the Earth}\)</span>?</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(1\over 12\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(1\over 3\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(1\over 6\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(1\over 4\)</span></span></label></p></div><div class="q-explanation"><p>The Moon has no atmoshere and a gravitational field strength that is one sixth of the Earth.</p><p>Since pressure is proportional to gravitational field strength, the pressure on the Moon is one sixth that on Earth. This is doubled since 10 m depth of water on Earth is equivalent to atmospheric pressure.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>This image is from a Geogebra simulation.</p><p style="text-align: center;"><img alt="" height="281" src="../../screenshot-2019-12-19-at-14.41.03.png" width="442"></p><p>Calculate <span class="math-tex">\(F_2\)</span>.</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>12 N</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.5 N</span></label> </p><p><label class="radio"> <input type="radio"> <span>6 N</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.75 N</span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\({F_1\over A_1}={F_2\over A_2}\Rightarrow F_2=F_1{A_2\over A_1}\)</span></p><p>Since <span class="math-tex">\({r_2\over r_1}=2\)</span>, <span class="math-tex">\({A_2\over A_1}=4\Rightarrow F_2=3\times 4\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>This image is from a Geogebra simulation.</p><p style="text-align: center;"><img alt="" height="278" src="../../screenshot-2019-12-19-at-14.50.52.png" width="357"></p><p>Calculate <span class="math-tex">\(\Delta h\)</span>.</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>20 m</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>2 m</span></label> </p><p><label class="radio"> <input type="radio"> <span>2 cm</span></label> </p><p><label class="radio"> <input type="radio"> <span>20 cm</span></label> </p></div><div class="q-explanation"><p>The pressure acting, <span class="math-tex">\(P = {20\over 10\times10^{-4}} = 20 \text{ kPa}\)</span></p><p>This pressure is equal to <span class="math-tex">\(\rho_f g\Delta h\)</span>:</p><p><span class="math-tex">\(\Delta h={20 000\over 1000\times 10}=2 \text{ m}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A rectangular block with square base of side 4 m and height 5 m is immersed in water in a room with no air.</p><p style="text-align: center;"><img alt="" height="224" src="../../screenshot-2019-12-19-at-16.10.43.png" width="269"></p><p>If the bottom of the block is at a depth of 10 m, the pressure on the bottom surface of the block is:</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>100 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>200 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>10 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>110 kPa</span></label> </p></div><div class="q-explanation"><p>Since no air is present, there is no atmospheric pressure. The depth of the bottom surface is 10 m.</p><p><span class="math-tex">\(P= ρ_fgd = 1000\times10\times10 = 100\text{ kPa}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A rectangular block with square base of side 4 m and height 5 m is immersed in water in a room with no air.</p><p style="text-align: center;"><img alt="" height="224" src="../../screenshot-2019-12-19-at-16.10.43.png" width="269"></p><p>If the bottom of the block is at a depth of 10 m, the pressure on the top surface of the block is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>500 kPa</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>50 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>150 kPa</span></label> </p><p><label class="radio"> <input type="radio"> <span>5 kPa</span></label> </p></div><div class="q-explanation"><p>Since no air is present, there is no atmospheric pressure. The depth of the top surface is 5 m.</p><p><span class="math-tex">\(P= ρ_fgd = 1000\times10\times5 = 50\text{ kPa}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A rectangular block with square base of side 4 m and height 5 m is immersed in water in a room with no air.</p><p style="text-align: center;"><img alt="" height="224" src="../../screenshot-2019-12-19-at-16.10.43.png" width="269"></p><p>If the bottom of the block is at a depth of 10 m, the buoyant force is:</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>800 kN</span></label> </p><p><label class="radio"> <input type="radio"> <span>80 kN</span></label> </p><p><label class="radio"> <input type="radio"> <span>200 kN</span></label> </p><p><label class="radio"> <input type="radio"> <span>50 kN</span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(B=\rho_fV_fg\)</span></p><p>The volume of fluid displaced is equal to the volume of block <span class="math-tex">\(= 4\times4\times5 = 80\text{ m}^3\)</span></p><p><span class="math-tex">\(B = 1000\times 80\times 10 = 800\text{ kN}\)</span></p><p>NB: The depth of the block is irrelevant once it becomes fully submerged.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> 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