Q. A horizontal pipe line carries water in streamline flow. At a point where the cross-sectional area is 10 c$m^{2}$ the water velocity is 1 m$s^{- 1}$ and pressure is 2000 Pa. The pressure of water at another point where the cross-sectional area is 5 c$m^{2}$, is
A) 200 Pa
B) 400 Pa
C) 500 Pa
D) 800 Pa
Explanation
(c) Since cross-sectional area is halved, therefore, velocity is doubled.
Now, $p_{1} = 2000Pa,\ v_{1} = 1{ms}^{- 1}$
$p_{2} = ?,v_{2} = 2{\ ms}^{- 1}$
${Again\ \ \ \ p}_{2} + \frac{1}{2} \times 1000 \times 2 \times 2 = 2000 + \frac{1}{2} \times 1000 \times 1 \times 1$
${or\ \ \ \ \ p}_{2} = 2000 + 500(1 - 4) = 500Pa$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.