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Question

In a horizontal pipeline of uniform cross-section the pressure falls by 8 N/m2 between two points separated by 1 km. If oil of density 800 kg/m3 flows through the pipe, find the change in K.E per kg of oil at these points.

A
102 J/kg
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B
103 J/kg
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C
104 J/kg
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D
101 J/kg
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Solution

The correct option is A 102 J/kg
Let P1 and P2 be the pressures at points 1 and 2 respectively on the horizontal pipe.P1P2=8 N/m2
h1=h2 ( pipe is horizontal)
By using bernoulli's equation,
P1V1+12mv21+mgh1=P2V2+12mv22+mgh2
For per unit volume, divide it by m and then we get
P1ρ+v212=P2ρ+v222
P1P2ρ=v22v212
Right side of above equation is the change in K.E unit mass
ΔK.E.=8800=1100=102 J/kg


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