Liquid pressure is the pressure exerted by a liquid on an object immersed in it or on the walls of its container, arising from the weight of the liquid column above. In everyday life, liquid pressure explains why the base of a dam must be constructed thicker than its top, why household water tanks are elevated, and how medical intravenous drips function.
See how the liquid pressure formula is derived, how depth and density affect manometer readings, and how two immiscible liquids balance in a U-tube.
A liquid column of height \(h\), base area \(A\) and density \(\rho\) has volume \(V = Ah\), mass \(m = Ah\rho\) and weight \(W = Ah\rho g\). Therefore, pressure at the base is:
Liquid pressure
\(P\) = liquid pressure, \(h\) = depth, \(\rho\) = density, \(g\) = gravitational acceleration.
At the common horizontal level containing points A and B, pressure is equal:
U-tube equilibrium
Measure \(h_1\) and \(h_2\) to compare the densities of two immiscible liquids.
Liquid pressure is the pressure exerted by a liquid on an object immersed in it or on the walls of its container, caused by the weight of the liquid column above.
For a liquid column of height \(h\), base area \(A\) and density \(\rho\): \(V = Ah\), \(m = Ah\rho\), \(W = Ah\rho g\). Therefore, \(P = \frac{W}{A} = h\rho g\).
Liquid pressure depends directly on depth \(h\), density \(\rho\), and gravitational acceleration \(g\).
When the liquid surface is open to the atmosphere, the total pressure experienced by an immersed object is \(\text{Actual pressure} = h\rho g + P_{\text{atm}}\).
Answer in your mind, then press “Check Answer”.
A fish is swimming at a depth of \(24\ \mathrm{m}\) in a freshwater lake. If the density of water is \(1\,000\ \mathrm{kg\,m^{-3}}\) and gravitational acceleration is \(9.81\ \mathrm{m\,s^{-2}}\), what is the water pressure experienced by the fish?
A diver dives to a depth of \(35\ \mathrm{m}\) in sea water of density \(1\,060\ \mathrm{kg\,m^{-3}}\). Given \(g = 9.81\ \mathrm{m\,s^{-2}}\) and atmospheric pressure is \(100\ \mathrm{kPa}\), calculate the actual pressure acting on the diver's body.
In a U-tube containing water of density \(1\,000\ \mathrm{kg\,m^{-3}}\) and olive oil, the height of the water column above the boundary level is \(15.0\ \mathrm{cm}\), while the height of the olive oil column is \(16.5\ \mathrm{cm}\). Find the density of the olive oil.
A wider container filled with water exerts higher water pressure at the bottom than a narrow tube of water at the exact same depth.
Liquid pressure depends strictly on depth \(h\), density \(\rho\), and \(g\). Base area, volume, and container shape have no effect on liquid pressure.
Pressure in a liquid acts only downwards onto the seabed or container base.
Liquid pressure acts in all directions equally at any given depth, which is why water shoots equally from holes on all sides at the same depth.
In a siphon, liquid moves because gravity pulls on the upper intake tube.
Liquid flows out at the lower exit because of the height difference, which creates a lower pressure region at the tube bend; external atmospheric pressure pushes water into the higher intake.
Objective: Identify the factors affecting liquid pressure, actual pressure, and applications of liquid pressure.
1 Which of the following factors affects the pressure at a specific point in a static liquid?
2 Why is the wall of a hydroelectric dam constructed significantly thicker at the base than at the top?
3 The formula to calculate the actual pressure experienced by an object submerged in a liquid open to the atmosphere is Actual pressure = hρg + .
4 The S.I. unit for pressure is the , which is equivalent to 1 N m⁻².
Match each liquid pressure phenomenon or application to its correct scientific principle or function. If using a phone, tap the answer first, then tap the matching box.
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