The water in a 25-m-deep reservoir is kept inside by a 90-m-wide wall whose cross section is an equilateral triangle, as shown in the figure. Find (a) the total force (hydrostatic $+$ atmospheric) acting on the inner surface of the wall and its line of action and (b) the magnitude of the horizontal component of this force. Take $P_{\mathrm{am}}=100\ \mathrm{kPa}$.

A pressure cooker cooks a lot faster than an ordinary pan by maintaining a higher pressure and temperature inside. The lid of a pressure cooker is well sealed, and steam can escape only through an opening in the middle of the lid. A separate metal piece, the petcock, sits on top of this opening and prevents steam from escaping until the pressure force overcomes the weight of the petcock. The periodic escape of the steam in this manner prevents any potentially dangerous pressure buildup and keeps the pressure inside at a constant value. Determine the mass of the petcock of a pressure cooker whose operation pressure is 120 kPa gage and has an opening cross-sectional area of $3 mm^2$. Assume an atmospheric pressure of 101 kPa, and draw the free-body diagram of the petcock.

A 3-m-high, 5-m-wide rectangular gate is hinged at the top edge at A and is restrained by a fixed ridge at B. Determine the hydrostatic force exerted on the gate by the 5 -m-high water and the location of the pressure center.

A 3-m-high, 6-m-wide rectangular gate is hinged at the top edge at A and is restrained by a fixed ridge at B. Determine the hydrostatic force exerted on the gate by the 5-m-high water and the location of the pressure center.

A 3 -m-wide, 8-m-high rectangular gate is located at the end of a rectangular passage that is connected to a large open tank filled with water as shown in the figure. The gate is hinged at its bottom and held closed by a horizontal force, $F_H$, located at the center of the gate. The maximum value for $F_H$ is $3500 \mathrm{kN}$. (a) Determine the maximum water depth, $h$, above the center of the gate that can exist without the gate opening. (b) Is the answer the same if the gate is hinged at the top? Explain your answer.

A 2-m-long and 3-m-wide horizontal rectangular plate is submerged in water. The distance of the top surface from the free surface is 5 m. The atmospheric pressure is 95 kPa. Considering atmospheric pressure, the hydrostatic force acting on the top surface of this plate is (a) 307 kN(b) 688 kN(c) 747 kN(d) 864 kN(e) 2950 kN

Determine the pressure exerted on the surface of a submarine cruising 225 ft below the free surface of the sea. Assume that the barometric pressure is 14.7 psia and the specific gravity of seawater is 1.03.

An elastic air balloon having a diameter of $30 \mathrm{~cm}$ is attached to the base of a container partially filled with water at $+4^{\circ} \mathrm{C}$, as shown in the figure. If the pressure of the air above the water is gradually increased from $100\ \mathrm{kPa}$ to $1.6\ \mathrm{MPa}$, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by $P=C D^n$, where $C$ is a constant and $n=-2$. The weight of the balloon and the air in it is negligible.

Consider a U–tube whose arms are open to the atmosphere. Now water is poured into the U–tube from one arm, and light oil $( ho = 790 kg/m^3)$ from the other. One arm contains 70–cm–high water, while the other arm contains bothfluids with an oil–to–water height ratio of 6. Determine the height of each fluid in that arm.

Consider a U-­tube whose arms are open to the atmosphere. Now water is poured into the U-­tube from one arm, and light oil $\left(\rho=790 \mathrm{kg} / \mathrm{m}^{3}\right)$ from the other. One arm con­tains 70­-cm-­high water, while the other arm contains both fluids with an oil­-to-­water height ratio of 4. Determine the height of each fluid in that arm.

On a day in which the local atmospheric pressure is $99.5\ \mathrm{kPa}$, answer each of the following: (a) Determine the column height of mercury in a mercury barometer in units of meters, feet, and inches. (b) Francis is concerned about mercury poisoning, so he builds a water barometer to replace the mercury barometer. Calculate the column height of water in the water barometer in units of meters, feet, and inches. $(c)$ Discuss why a water barometer is not very practical. (d) Ignoring the practicality issue, which of the two (mercury or water) would be more precise? Explain.

The piston of a vertical piston-cylinder device containing a gas has a mass if 60 kg and a cross-sectional area of 0.04 m^2. The local atmospheric pressure is 0.97 bar, and the gravitational acceleration is 9.81 m/s^2. Determine the pressure inside the cylinder.

Consider the system shown in the figure. If a change of $0.9\ \mathrm{kPa}$ in the pressure of air causes the brine-mercury interface in the right column to drop by $5 \mathrm{~mm}$ in the brine level in the right column while the pressure in the brine pipe remains constant, find the ratio of $A_2 / A_1$.

Consider a U-tube whose arms are open to the atmosphere. Now water is poured into the U-tube from one arm, and light oil ($\rho$= 790 kg/m^3) from the other. One arm contains 70-cm high water, while the other arm contains both fluids with an oil-to-water height ratio of 4. Determine the height of each fluid in that form.