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 inclined-tube manometer shown has $D=96 \mathrm{~mm}$ and $d=8 \mathrm{~mm}$. Determine the angle, $\theta$, required to provide a $5: 1$ increase in liquid deflection, $L$, compared with the total deflection in a regular U-tube manometer. Evaluate the sensitivity of this inclined-tube manometer.

The polysulfone block is glued at its top and bottom to the rigid plates. If a tangential force, applied to the top plate, causes the material to deform so that its sides are described by the equation $y=3.56 x^{1 / 4},$ determine the shear strain at the corners $A$ and $B .$

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) $147 ~\mathrm{kN}$

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) $45 ~\mathrm{kPa}$

A swimming pool is filled with $2 \mathrm{~m}$ of water. Its bottom is square and measures $4 \mathrm{~m}$ on a side. Two opposite sides are vertical; one end is at $45^{\circ}$ and the other makes an angle of $60^{\circ}$ with the horizontal. Calculate the force of the water on: (a) The bottom (b) A vertical side (c) The $45^{\circ}$ end (d) The $60^{\circ}$ end

The top of each gate shown in figure lies $4 \mathrm{~m}$ below the water surface. Find the location and magnitude of the force acting on one side assuming a vertical orientation.

The sides of a triangular area measure $2 \mathrm{~m}, 3 \mathrm{~m}$, and $3 \mathrm{~m}$, respectively. Calculate the force of water on one side of the area if the 2-m side is horizontal and $10 \mathrm{~m}$ below the surface and the triangle is: (a) Vertical (b) Horizontal (c) On a $60^{\circ}$ angle sloped upward.

The 150-lb man lies against the cushion for which the coefficient of static friction is $\mu_s=0.5$. Determine the resultant normal and frictional forces the cushion exerts on him if, due to rotation about the z axis, he has a constant speed v=20 ft / s. Neglect the size of the man. Take $\theta=60^{\circ}$.

Crates A and B weigh 100 lb and 50 lb, respectively. If they start from rest, determine their speed when t = 5 s. Also, find the force exerted by crate A on crate B during the motion. The coefficient of kinetic friction between the crates and the ground is $\mu_k = 0.25$.

Three parallel bolting forces act on the circular plate. Determine the resultant force, and specify its location (x, z) on the plate. $F_A=200 lb , F_B=100 lb$, and $F_C=400 lb$

A cylindrical tank is fully filled with water. In order to increase the flow from the tank, additional pressure is applied to the water surface by a compressor. For $P_0=0, P_0=5$ bar, and $P_0=10$ bar, find the hydrostatic force on the surface $A$ exerted by water.

Determine the time needed to pull the cord at B down 4 ft starting from rest when a force of 10 lb is applied to the cord. Block A weighs 20 lb. Neglect the mass of the pulleys and cords.