In a horizontal pipeline of uniform cross-section the pressure falls by 8N/m2 between two points separated by 1km. If oil of density 800kg/m3 flows through the pipe, find the change in K.E per kg of oil at these points.
A
10−2J/kg
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B
10−3J/kg
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C
10−4J/kg
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D
10−1J/kg
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Solution
The correct option is A10−2J/kg Let P1 and P2 be the pressures at points 1 and 2 respectively on the horizontal pipe.P1−P2=8N/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 P1−P2ρ=v22−v212 Right side of above equation is the change in K.E unit mass ΔK.E.=8800=1100=10−2J/kg