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Question

A liquid of density ρ is coming out of a hose pipe of radius a with horizontal speedvand hits a mesh.50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and25% comes back with the same speed. The resultant pressure on the mesh will be:


A

ρv2

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B

3/4ρv2

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C

1/2ρv2

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D

1/4ρv2

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Solution

The correct option is B

3/4ρv2


Step 1: Given data

% of liquid which passes unaffected =50%

% of liquid which looses its momentum =25%

% of liquid which come back with same speed=25%

Step 2: The resultant pressure on the mesh

Momentum per second carried by liquid per second =ρav2Where,v=speed,a=area,ρ=densityofliquid

net force due to reflected liquid =2×[1/4ρav2]

net force due to stopped liquid =1/4ρav2

Total force =2×[1/4ρav2]+[1/4ρav2]

=(3/4)ρav2

Therefore, pressure, P=forcearea

=(3/4)ρav2a=(3/4)ρv2

Hence, option (B) is correct.


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