Q: A horizontal pipe line carries water in a streamline flow. At a point along the pipe where the cross-sectional area is 10 cm2, the velocity of water is 1 m/s and the pressure is 2000 Pa. What is the pressure at another point where the cross-sectional area is 5 cm2.
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Sol: According to equation of continuity
A1 v1 = A2 v2
v2 = (10/5) × 1 =2m/s
Now, according to Bernoulli’s equation,
$\large P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2 $ (∵ horizontal pipe)
$\large 2000 + \frac{1}{2}\times 10^3 \times 1^2 = P_2 + \frac{1}{2}\times 10^3 \times 2^2 $
P2 = 500 Pa