A reservoir dam has a vertical surface in contact with the water that is 125 m wide and 11.0 m high. Air pressure is one atmosphere. If the reservoir is completely filled, determine the magnitude of the net force acting on the dam. (Hint: Since the pressure varies linearly with depth, you will need to use your knowledge of calculus in order to determine the force on the dam due to water. Use 1.00 ✕ 103 kg/m3 for the density of water.)

The answer to the question is;

The net force acting on the dam is 73,001,115 N.

Explanation:

To solve he question, we note that

Pressure = Force/Area and the formula for pressure is

Pressure = hρg

While force, F= Pressure × Area

For a small area at the bottom of the dam we have

= hρg×dh×width

Where

w = width of the dam = 125 m

ρ = Density of water = 1.0×10³ m³

g = Acceleration due to gravity = 9.81 m/s²

h = Height  of the dam = 11.0 m

Therefore force over the dam wall =  =  

                                   = [ 11²/2×1×10³×9.81×125] - 0

                                = 73,001,115 N

The net force acting on the dam = 73,001,115 N.

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