SSC JE Mechanical Engineering 25 Sep 2019 Shift 1 Paper

Question : 177 of 200

Marks: +1, -0

A 20 m high dam is filled with water up to the top. The force acting on the vertical dam wall (20 m high × 25 m wide) is given as (consider the density of water = 1000 kg/m

^{3}

; g = acceleration due to gravity):

50,000/g kN
1000 kN
5g MN
25,000 N

Validate

Solution:

Force on the dam wall (F) = Pressure at the center (P) × Projected area of the dam (A) = ρgAx̅
The pressure at the center (P) = ρ × g × x̅

Given:
Height of the dam (H) = 20 m
Height of the centroid from the water surface (x̅) = H/2 = 10 m
Density of water (ρ) = 1000 kg/m

^3

Width of dam (w) = 25 m
Area of dam (A) = 20 × 25 = 500 m

^{2}

F = P × A = (ρ × g × h̅)

× 500 = (5 × 106 × g) = 5g MN

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