A horizontal pipelline carries water in a streamline flow . At a point along the pipe , where the cross - sectional area is `10 cm^(2)` , the water velocity is 1 m/s and pressure is 2000 Pa . The pressure of water at another point where cross - sectional area is ` 5 cm^(2)` , is _______ (in Pa)

Options

A. 4000 Pa
B. 2000 Pa
C. 1000 Pa
D. 500 Pa

Answer

D

Explanation

From continuity equation
`A_1 V_1=A_2 V_2`
`implies 10xx1=5xxV_2 implies V_2=2 m//s`
According to bernoulli.s Principle-
`P_1+1/2 rho V_1^2=P_2+1/2 rho V_2^2`
`implies P_2=P_1+1/2 rho(V_1^2-V_2^2)`
`=2000+1/2 xx 10^3(1^2-2^2)`
=2000-1500=500 Pa.