Question

Water is flowing through a horizontal pipe of variable cross - section. The rate of volume flow is 0.2 lit /sec. The pressure is 30,000 Pa. at a point where the area of cross - section is 5 $\times$ ${10}^{-5}$ $m^2$. The pressure at the point where the area of cross- section is ${10}^{-4}$ is

• A. 6000 Pa
• B. 36000 Pa
• C. 24000 Pa
• D. 30000 Pa

Answer 1

The correct option is B 36000 Pa

Volume rate = $0.2\mu /s$
$=0.2\times {10}^{-3}m/s$
$A_1{V}_1=A{V}_2=0.2\times {10}^{-3}$
$V_1=\frac{0.2\times {10}^{-3}}{5\times {10}^{-5}}=4$
$V_2=\frac{0.2\times {10}^{-3}}{{10}^{-4}}=2$
Bernaulli's principle -
$P_1+\frac{1}{2}P{V}_1^2=P_2+\frac{1}{2}P{V}_2^2$
$P_2=P_1+\frac{1}{2}P(V_1^2-V_2^2)$
$=30000+\frac{1}{2}\times {10}^3(4^2-2^2)$
$=30000+\frac{1}{2}\times {10}^3(16-4)$
$=30000+\frac{12}{2}\times {10}^3$
$=30000+6000$
$=36000Pa$