Find the force $P$ required to hold the gate in the position shown in Fig. The gate is $5 \mathrm{~m}$ wide.

Gate $A B$ in Fig. P2.61 is a homogeneous mass of $180 \mathrm{~kg}$, $1.2 \mathrm{~m}$ wide into the paper, hinged at $A$, and resting on a smooth bottom at $B$. All fluids are at $20^{\circ} \mathrm{C}$. At what water depth $h$ will the force at point $B$ will be zero?

The flow of water from a reservoir is controlled by a 5-ft-wide L-shaped gate hinged at point A, is desired that the gate open when the water height is 12 ft, determine the mass of the required weight W.

What $P$ is needed to hold the $4$-$\mathrm{m}$-wide gate shown in Fig. closed?

Gate $A B$ in Fig. P2.55 is $5\ \mathrm{ft}$ wide into the paper, hinged at $A$, and restrained by a stop at $B$. The water is at $20^{\circ} \mathrm{C}$. Determine $(a)$ the force on stop $B$ and $(b)$ the reactions at $A$ if the water depth $h=9.5\ \mathrm{ft}$.

Determine the magnitude and direction of the anchoring force needed to hold the horizontal elbow and nozzle combination shown in Fig. P5.45 in place. Atmospheric pressure is 100 kPa (abs). The gauge pressure at section (1) is 100 kPa. In section (2), the water exits into the atmosphere.

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) $1.0 \mathrm{~m} ?$

In Fig. P2.55, gate $AB$ is $5 \ \text{ft}$ wide into the paper, and stop $B$ will break if the water force on it equals $9200 \ \text{lbf}$. At what depth $h$, this condition will reach?

In Fig. P2.58, the cover gate $A B$ closes a circular opening $80 \mathrm{~cm}$ in diameter. The gate is held closed by a $200$-$\mathrm{kg}$ mass as shown. Assuming the standard gravity at $20^{\circ} \mathrm{C}$. What will be the water level $h$ at which the gate is dislodged? Neglecting the weight of the gate.

Find the force $P$ needed to just open the gate shown in Fig. if: (a) $H=6 \mathrm{~m}, R=2 \mathrm{~m}$, and the gate is $4 \mathrm{~m}$ wide. (b) $H=20 ~\mathrm{ft}, R=6 ~\mathrm{ft}$, and the gate is $12 ~\mathrm{ft}$ wide.

For the curved surface $A B$ :

a. Find the magnitude, direction, and line of action of the vertical component of hydrostatic force acting on the surface. Here $\ell=1 \mathrm{~m}$. b. Find the magnitude, direction, and line of action of the horizontal component of hydrostatic force acting on the surface. c. Find the resultant hydrostatic force acting on the surface.

A vertical gate at the end of a channel opens when the water above the hinge produces a moment greater than the moment of the water below the hinge. What height $h$ of water is needed to open the gate if: (a) $H=0.9 \mathrm{~m}$ (b) $H=1.2 \mathrm{~m}$ (c) $H=1.5 \mathrm{~m}$

A large, open tank contains water and is connected to a 6-ft-diameter conduit as shown in the given figure. A circular plug is used to seal the conduit. Determine the magnitude, direction, and location of the force of the water on the plug.

A rectangular gate (width $w=2 \mathrm{~m}$ ) is hinged as shown, with a stop on the lower edge. At what depth $H$ will the gate tip?