A normal force of \(480\,\mathrm{N}\) acts uniformly on area \(0.12\,\mathrm{m^2}\). Find the pressure.

A fluid pressure of \(2.5\times10^5\,\mathrm{Pa}\) acts on a small piston of area \(0.030\,\mathrm{m^2}\). Find the normal force.

Find the gauge pressure \(2.0\,\mathrm{m}\) below the surface of water with density \(1000\,\mathrm{kg\,m^{-3}}\).

Oil of density \(840\,\mathrm{kg\,m^{-3}}\) is open to the atmosphere. Find the absolute pressure \(3.5\,\mathrm{m}\) below the surface, using \(p_{\mathrm{atm}}=1.01\times10^5\,\mathrm{Pa}\).

In seawater of density \(1030\,\mathrm{kg\,m^{-3}}\), find the pressure increase from depth \(1.2\,\mathrm{m}\) to depth \(4.7\,\mathrm{m}\).

At what depth in water is the gauge pressure \(35\,\mathrm{kPa}\)? Use \(\rho=1000\,\mathrm{kg\,m^{-3}}\).

A flat hatch of area \(0.80\,\mathrm{m^2}\) is small enough that all points are effectively \(6.0\,\mathrm{m}\) below a water surface. Find the net force due to gauge pressure.

At the same depth, compare the gauge pressure in water \((1000\,\mathrm{kg\,m^{-3}})\) with that in oil \((780\,\mathrm{kg\,m^{-3}})\). Find \(p_{\mathrm{water}}/p_{\mathrm{oil}}\).

A cylindrical tank of radius \(0.30\,\mathrm{m}\) holds water to depth \(0.50\,\mathrm{m}\). Find the net gauge-pressure force on the flat bottom.

A tank is open to the atmosphere and contains \(0.60\,\mathrm{m}\) of oil \((820\,\mathrm{kg\,m^{-3}})\) above \(0.40\,\mathrm{m}\) of water. Find the gauge pressure at the bottom.

A mercury manometer shows a height difference of \(0.18\,\mathrm{m}\). Taking mercury density as \(1.36\times10^4\,\mathrm{kg\,m^{-3}}\), find the pressure difference between the two sides.

The gas above a liquid in a sealed tank is at absolute pressure \(1.40\times10^5\,\mathrm{Pa}\). The liquid density is \(950\,\mathrm{kg\,m^{-3}}\). Find the absolute pressure \(2.0\,\mathrm{m}\) below the liquid surface.

A small piston of area \(4.0\times10^{-3}\,\mathrm{m^2}\) is pushed with \(120\,\mathrm{N}\). The same static pressure is transmitted to a larger piston of area \(6.0\times10^{-2}\,\mathrm{m^2}\). Find the force on the larger piston.

A small slanted window of area \(0.15\,\mathrm{m^2}\) has all points approximately \(4.0\,\mathrm{m}\) below a water surface. Find the gauge-pressure force and state its direction relative to the window.

A vertical rectangular gate of width \(1.2\,\mathrm{m}\) and height \(2.0\,\mathrm{m}\) has its top edge at the water surface. Derive and calculate the resultant gauge-pressure force on one face.

A vertical rectangular inspection plate has width \(0.80\,\mathrm{m}\), height \(1.5\,\mathrm{m}\), and top edge at depth \(3.0\,\mathrm{m}\) in water. Derive the resultant gauge-pressure force.

A static fluid has density \(\rho(y)=\rho_0(1+\alpha y)\), where \(y\) is depth measured downward from the surface. Derive the gauge pressure at depth \(h\). State the assumption behind the differential equation you use.

A cylinder of cross-sectional area \(A\) and height \(L\) is fully submerged in a constant-density fluid. Its top is at depth \(h\). Use pressure forces on the top and bottom faces to derive the net upward force.

A vertical rectangular window of width \(w\) and height \(H\) can tolerate resultant gauge-pressure force \(F_{\max}\). Its top edge is at depth \(h_0\) in a liquid of density \(\rho\). Derive the largest allowed \(h_0\).

For any flat vertical plate in a constant-density fluid, let \(h\) be depth over the plate and \(\bar h\) be the depth of its centroid. Show that the resultant gauge-pressure force magnitude is \(\rho gA\bar h\). Explain what this result does not tell you.