Question

A dam which is v = 21 meters tall has an outflow gate. The gate, height u = 4 meters, has a shape given by the region under the equation, y = u − x², y ≥ 0. Note that y is the vertical distance from the bottom of the gate in meters, and x is the horizontal distance from the middle, measured in meters.



If the entire dam is under water (That is, the surface of the water is at the top of the dam), what is the total hydrostatic force outward on the gate?
Note, here ρ is the density of water, and g the gravitational constant.

(A)

21

∫

0

ρgy

√

4 − y2

 dy (B)

4

∫

0

2ρg(21 − y)

√

4 − y2

 dy (C)

4

∫

0

2ρg(21 − y)

√

4 − y

 dy (D)

4

∫

0

ρgy^3/2dy (E)

4

∫

0

ρg(21 − y)

√

4 − y

 dy (F)

4

∫

0

2ρg(y − 21)

√

4 − y

 dy (G)

21

∫

0

ρgy

√

4 − y

 dy (H)

21

∫

0

2ρgy

√

4 − y

 dy

Answer 1