Problem

Determine the magnitude and the location of the hydrostatic force on the 2-m by 4-m vertic...

Determine the magnitude and the location of the hydrostatic force on the 2-m by 4-m vertical rectangular gate shown in Figure 3.6.3. The top of the gate is 6 m below the water surface.

Figure 3.6.3 Vertical rectangular gate for example 3.6.3.

EXAMPLE 3.6.3

Consider a vertical rectangular gate (b = 4 m and h = 2 m) that is vertically submerged in water so that the top of the gate is 4 m below the surface of the water (as shown in Figure 3.6.3). Determine the total resultant force on the gate and the location of the center of pressure.

SOLUTION

Use the free-body diagram in Figure 3.6.3. The total resultant force is computed using equation (3.6.2), F = γhcA, where hc = 4 + (2/2) = 5m:

The location of the center of pressure is computed using equation (3.6.8):

Alternatively, this problem can be solved by the simple integration , where dA = 4 dy:

Figure 3.6.2 Hydrostatic force on dam for example 3.6.2.

EXAMPLE 3.6.2

Determine the hydrostatic force and the location of the center of pressure on the 25 m long dam shown in Figure 3.6.2. The face of the dam is at angle of 60°. Assume 20°C.

SOLUTION

The diagram in Figure 3.6.2 shows the pressure distribution. Using equation (3.6.2), hc = 2.5 m and A = (25 m × 5)/sin 60°, so the hydrostatic force is