Question

A horizontal pipe line carries water in a streamline flow. At a point along the pipe where the cross sectional area is $10c{m}^2$, the water velocity is $1m{s}^{-1}$ and the pressure is $2000Pa$. What is the pressure at another point where the cross sectional area is $5c{m}^2$ ?

• 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 $10c{m}^2\times 1m{s}^{-1}=5c{m}^2\times v_2$
$\therefore v_2=2m{s}^{-1}$
Using Bernoulli's theorem for horizontal flow,
$p_2+\frac{1}{2}\rho v_2^2=p_1+\frac{1}{2}\rho v_1^2$
or$p_2+\frac{1}{2}\times 10^3\times 2^2=2000+\frac{1}{2}\times 10^3\times 1^2$
or$p_2=2000+500-2000=500pa.$