Calculate the force $P$ necessary to hold the $\textrm{4-m}$ wide gate in the position shown in Fig. if: (a) $H=6 \mathrm{~m}$ (b) $H=8 \mathrm{~m}$ (c) $H=10 \mathrm{~m}$

Semicircular plane gate $A B$ is hinged along $B$ and held by horizontal force $F_{\mathrm{A}}$ applied at $A$. The liquid to the left of the gate is water. Calculate the force $F_{\mathrm{A}}$ required for equilibrium.

The tank, with an initial pressure of $p=20 ~\mathrm{kPa}$, is accelerated as shown in Fig. at the rate of 5 $~\mathrm{m} / \mathrm{s}^2$. The force on the $\textrm{4-cm}$-diameter plug is nearest: (A) $30 \mathrm{~N}$ (B) $50 \mathrm{~N}$ (C) $130 \mathrm{~N}$ (D) $420 \mathrm{~N}$

The rectangular barge of Fig. is known to be $15 \mathrm{~m}$ long. A load having a mass of $900 \mathrm{~kg}$ is added to the barge causing it to sink $10 \mathrm{~mm}$. How wide is the barge? (A) $6 \mathrm{~m}$ (B) $9.2 \mathrm{~m}$ (C) $7.5 \mathrm{~m}$ (D) $0.62 \mathrm{~m}$

A gate having the shape shown is located in the vertical side of an open tank containing water. The gate is mounted on a horizontal shaft, (a) When the water level is at the top of the gate, determine the magnitude of the fluid force on the rectangular portion of the gate above the shaft and the magnitude of the fluid force on the semicircular portion of the gate below the shaft. (b) For this same fluid, depth determine the moment of the force acting on the semicircular portion of the gate with respect to an axis that coincides with the shaft.

A force $P=300 ~\mathrm{kN}$ is needed to just open the gate of Fig. with $R=1.2 \mathrm{~m}$ and $H=4 \mathrm{~m}$. How wide is the gate? (A) $2.98 \mathrm{~m}$ (B) $3.67 \mathrm{~m}$ (C) $4.32 \mathrm{~m}$ (D) $5.16 \mathrm{~m}$

An open tank has a vertical partition and on one side contains gasoline with a density $\mathrm{p}=700 \mathrm{kg} / \mathrm{m}^{3}$ at a depth of 4 m. A rectangular gate that is 4 m high and 2 m wide and hinged at one end is located in the partition. Water is slowly added to the empty side of the tank. At what depth, h, will the gate start to open?

At what height $H$ will the rigid gate, hinged at a central point as shown in Fig., open if $h$ is: (a) $0.6 \mathrm{~m}$ ? (b) $0.8 \mathrm{~m}$ ? (c) $1.0 \mathrm{~m} ?$

The rigid gate, $O A B$, of the given figure is hinged at $O$ and rests against a rigid support at $B$. What minimum horizontal force, $P$, is required to hold the gate closed if its width is $3 \mathrm{~m}$? Neglect the weight of the gate and friction in the hinge. The back of the gate is exposed to the atmosphere.

The rectangular gate shown in Fig. is $3 \mathrm{~m}$ wide. The force $P$ needed to hold the gate in the position shown is nearest: (A) $24.5 ~\mathrm{kN}$ (B) $32.7 ~\mathrm{kN}$ (C) $98 ~\mathrm{kN}$ (D) $147 ~\mathrm{kN}$

A partitioned tank as shown contains water and mercury. What is the gage pressure in the air trapped in the left chamber? What pressure would the air on the left need to be pumped to in order to bring the water and mercury free surfaces level?

The pressure in the foothills of the Rockies near Boulder, Colorado is $84 ~\mathrm{kPa}$. The pressure, assuming a constant density of $1.00 ~\mathrm{~kg} / \mathrm{m}^3$, at the top of a nearby $4000$-$\mathrm{m}$-$\mathrm{high}$ mountain is closest to: (A) $60~ \mathrm{kPa}$ (B) $55 ~\mathrm{kPa}$ (C) $50 ~\mathrm{kPa}$ (D) $45 ~\mathrm{kPa}$

Your pressure gauge indicates that the pressure in your cold tires is 0.25 MPa gage on a mountain at an elevation of 3500 m. What is the absolute pressure? After you drive down to sea level, your tires have warmed to 25$^{\circ} \mathrm{C}$. What pressure does your gauge now indicate? Assume a U.S. Standard Atmosphere.

Consider a cylindrical water tank of constant cross section A. Water is pumped into the tank at a constant rate k and leaks out through a small hole of area a in the bottom of the tank. From Torricelli’s principle in hydrodynamics (see Problem 6 in Section 2.3)it follows that the rate at which water flows through the hole isαa2gh, where h is the current depth of water in the tank,g is the acceleration due to gravity,andαis a contraction coefficient that satisfies 0.5≤α≤1.0.(a) Show that the depth of water in the tank at any time satisfies the equation dh/dt=(k−αa2gh)/A.(b) Determine the equilibrium depth he of water,and show that it is asymptotically stable.Observe that he does not depend on A.