Question

The 10 foot wide circle quarter gate AB is articulated at A. Determine the contact force between the gate and the smooth surface at B due to the pressure of the water acting on the gate. Use γ = 62.4 lb / ft^3 for the water. R=8 ft

Answer 1

Answer:

$F = 641,771.52 \dfrac{lb-ft}{s^2}$

Explanation:

Given that

R=8 ft

Width= 10 ft

We know that hydro statics force given as

  F=ρ g A X

ρ is the density of fluid

A projected area on vertical plane

X is distance of center mass of projected plane from free surface of water.

Here

X=8/2  ⇒X=4 ft

A=8 x 10=80  $ft^2$

So now putting the values

F=ρ g A X

F=62.4(32.14)(80)(4)

$F = 641,771.52 \dfrac{lb-ft}{s^2}$