1
Gate AB in Fig. P2.51 is 1.2 m long and 0.8 m into the paper. Neglecting atmospheric-pressure effects, compute the force F on the gate
2
Gate AB in Fig. P2.51 is 1.2 m long and 0.8 m into the paper. Neglecting atmospheric-pressure effects, compute its center of pressure position X.
3
A vertical lock gate is 4 m wide and separates 20°C water levels of 2 m and 3 m, respectively. Find the moment about the bottom required to keep the gate stationary.
4
Panel ABC in the slanted side of a water tank (shown at right) is an isoceles triangle with vertex at A and base BC = 2 m. Find the water force on the panel.
5
Panel ABC in the slanted side of a water tank (shown at right) is an isoceles triangle with vertex at A and base BC = 2 m. Find its line of action.
6
Gate AB in Fig. P2.55 is 5 ft wide into the paper, hinged at A, and restrained by a stop at B. Compute (a) the force on stop B
7
Gate AB in Fig. P2.55 is 5 ft wide into the paper, hinged at A, and restrained by a stop at B. Compute (b) the reactions at A if h = 9.5 ft.
8
For the gate of Prob. 2.55 above, stop “B” breaks if the force on it equals 9200 lbf. For what water depth h is this condition reached?
9
The tank in Fig. P2.57 is 2 m wide into the paper. Neglecting atmospheric pressure, find the resultant hydrostatic force on panel BC, (a) from a single formula
10
The tank in Fig. P2.57 is 2 m wide into the paper. Neglecting atmospheric pressure, find the resultant hydrostatic force on panel BC, (b) by computing horizontal and
vertical forces separately, in the spirit of curved surfaces.
11
In Fig. P2.58, weightless cover gate AB closes a circular opening 80 cm in diameter when weighed down by the 200-kg mass shown. What water level h will dislodge the gate?
12
The pressure in the air gap is 8000 Pa gage. The tank is cylindrical. Calculate the net hydrostatic force (a) on the bottom of the tank;
13
The pressure in the air gap is 8000 Pa gage. The tank is cylindrical. Calculate the net hydrostatic force (b) on the cylindrical sidewall CC;
14
The pressure in the air gap is 8000 Pa gage. The tank is cylindrical. Calculate the net hydrostatic force (c) on the annular plane panel BB.
15
Gate AB in Fig. P2.61 is a homogeneous mass of 180 kg, 1.2 m wide into the paper, resting on smooth bottom B. All fluids are at 20°C. For what water depth h will the force at point B be zero?
16
Gate AB in Fig. P2.62 is 15 ft long and 8 ft wide into the paper, hinged at B with a stop at A. The gate is 1-in-thick steel, SG = 7.85. Compute the 20°C water level h for which the gate will start to fall.
17
The tank in Fig. P2.63 has a 4-cm- diameter plug which will pop out if the hydrostatic force on it reaches 25 N. For 20°C fluids, what will be the reading h on the manometer when this happens?
18
Gate ABC in Fig. P2.64 has a fixed hinge at B and is 2 m wide into the paper. If the water level is high enough, the gate will open. Compute the depth h for which this happens.
19
Gate AB in Fig. P2.65 is semi-circular, hinged at B, and held by a horizontal force P at point A. Determine the required force P for equilibrium.
20
Dam ABC in Fig. P2.66 is 30 m wide into the paper and is concrete (SG ≈ 2.40). Find the hydrostatic force on surface AB and its moment about C. Could this force tip the dam over? Would fluid seepage under the dam change your argument?
21
Isosceles triangle gate AB in Fig. P2.68 is hinged at A and weighs 1500 N. What horizontal force P is required at point B for equilibrium?
22
Panel BCD is semicircular and line BC is 8 cm below the surface. Determine (a) the hydrostatic force on the panel
23
Panel BCD is semicircular and line BC is 8 cm below the surface. Determine (b) the moment of this force about D.
24
The cylindrical tank in Fig. P2.70 has a 35-cm-high cylindrical insert in the bottom. The pressure at point B is 156 kPa. Find (a) the pressure in the air space;
25
The cylindrical tank in Fig. P2.70 has a 35-cm-high cylindrical insert in the bottom. The pressure at point B is 156 kPa. Find (b) the force on the top of the insert. Neglect air pressure outside the tank.
26
In Fig. P2.71 gate AB is 3 m wide into the paper and is connected by a rod and pulley to a concrete sphere (SG =2.40). What sphere diameter is just right to close the gate?
27
Gate B is 30 cm high and 60 cm wide into the paper and hinged at the top. What is the water depth h which will first cause the gate to open?
28
Weightless gate AB is 5 ft wide into the paper and opens to let fresh water out when the ocean tide is falling. The hinge at A is 2 ft above the freshwater level. Find h when the gate opens.
29
Find the height H in Fig. P2.74 for which the hydrostatic force on the rectangular panel is the same as the force on the semicircular panel below. Find the force on each panel and set them equal:
30
Panel BC in Fig. P2.76 is circular. Compute (a) the hydrostatic force of the
water on the panel
31
Panel BC in Fig. P2.76 is circular. Compute (b) its center of pressure;
32
Panel BC in Fig. P2.76 is circular. Compute (c) the moment of this force about
point B.
33
Circular gate ABC is hinged at B. Compute the force just sufficient to keep the gate from opening when h = 8 m. Neglect atmospheric pressure.
34
Gate ABC in Fig. P2.79 is 1-m- square and hinged at B. It opens automatically when the water level is high enough. Neglecting atmospheric pressure, determine the lowest level h for which the gate will open. Is your result independent of the liquid density?
35
For the closed tank of Fig. P2.80, all fluids are at 20°C and the air space is pressurized. If the outward net hydrostatic force on the 40-cm by 30-cm panel at the bottom is 8450 N, estimate (a) the pressure in the air space;
36
For the closed tank of Fig. P2.80, all fluids are at 20°C and the air space is pressurized. If the outward net hydrostatic force on the 40-cm by 30-cm panel at the bottom is 8450 N, estimate (b) the reading h on the manometer.
37
Gate AB is 7 ft into the paper and weighs 3000 lbf when submerged. It is hinged at B and rests against a smooth wall at A. Find the water level h which will just cause the gate to open.
38
The dam in Fig. P2.82 is a quarter-circle 50 m wide into the paper. Determine the horizontal and vertical components of hydrostatic force against the dam
39
The dam in Fig. P2.82 is a quarter-circle 50 m wide into the paper. Determine the point CP where the resultant strikes the dam.
40
Gate AB is a quarter-circle 10 ft wide and hinged at B. Find the force F just sufficient to keep the gate from opening. The gate is uniform and weighs 3000 lbf.
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