A trough is filled with a liquid of density 875 kg/m3. The ends of the trough are equilateral triangles with sides 6 m long and vertex at the bottom. Find the hydrostatic force on one end of the trough. (Use 9.8 m/s2 for the acceleration due to gravity.)

The force on one end of the trough is 5.4 X 10⁵ N

Explanation:

The triangle is equilateral which means all the interior angles are 60° and the sides are 6m long.

According to the figure,

AI / 8 = sin (60) = √3/2

AI = 4√3

The depth of the water is AI = 4√3

The interval becomes, | 0 , 4√3|

w = 2JK

                        (the hydrostatic force acting on the strip is the product of the pressure and the area)

where.

ρ = 875 kg/m³

g = 9.8m/s²

d = depth ( d = y')

limit is 0 → 4√3

On solving the equation, we get the value of limit as 32√3

Therefore, the force on one end of the trough is 5.4 X 10⁵ N

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