Question

The water behind Grand Coulee Dam is 1200 m wide & 150 m deep. Find hydrostatic force on back of dam. (total force = avg pressure × area) 
a.5.2×109 N b. 8.8 × 1010 N c. 2 × 1010 N d. 18.0 × 1010 N 


Answer 1

TOTAL FORCE ON THE BACK OF THE DAM:

GIVEN:

Width of the dam, w= 1200m

Depth of the dam. d= 150m

Acceleration due to gravity, g= 9.8m/s

Density of water,

APPROACH:

The force exerted by the water on the back of the dam is not uniform (since the pressure varies linearly with height) and thus force decreases as height increases.

• The relationship between pressure and height is given as,

where is the density of the liquid, is the acceleration due to gravity and is the height/depth of the point.

• The relationship between force and pressure is given by,

where is the area of cross-section and is the average pressure. (We take average pressure since the pressure isn't uniform).

SOLUTION:

Force exerted on the back of the dam,

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