Question

A horizontal pipe line 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 $1\, ms ^{-1}$ and the pressure is $2000\, Pa$. What is the pressure at another point where the cross sectional area is $5 \,cm ^{2}$ ?

• A. 500 Pa
• B. 5 Pa
• C. 50 Pa
• D. 0.05 Pa

Answer 1

Answer: (A)

According to the equation of continuity,
$a_{1}\,v_{1}=a_{2}\,v_{2}$ or $10\, cm^{2} \times1 \,ms^{-1}=5\,cm^{2}\times v_{2}$
$\therefore \quad v_{2} = 2 \,ms^{-1}$
Using Bernoulli's theorem for horizontal flow,
$p_{2}+\frac{1}{2}\rho v^{2}_{2}=p_{1}+\frac{1}{2}\rho v^{2}_{1}$
or$\quad p_{2}+\frac{1}{2}\times10^{3}\times2^{2}=2000+\frac{1}{2}\times10^{3}\times1^{2}$
or$\quad p_{2}=2000+500-2000=500 \,pa.$