Question

An incompressible fluid is flowing steadily through a horizontal pipe of non-uniform cross section. If pressure of water is $4\times {10}^{4}N.m^{-2}$ at a point where cross section is $0.02m^2$ and velocity of flow is $2m{s}^{-1}$, the pressure at a point of cross sectional area $0.01m^2$ in $N.m^{-2}$ is :

• A. $4.6\times {10}^4$
• B. $3.4\times {10}^4$
• C. $4\times {10}^4$
• D. $2\times {10}^4$

Answer 1

The correct option is B $3.4\times {10}^4$

From continuity theorem,
$A_1{V}_1=A_2{V}_2$
$2\times 0.02=0.01\times V_2$
$V_2=4m/s$

Applying Bernoulli equation across different point,
$4\times {10}^4+\frac{1}{2}\times 1000\times 4=p_2+\frac{1}{2}\times 1000\times 16$
$4\times {10}^4-\frac{1}{2}\times 1000\times 12=p_2$
$4\times {10}^4-6000=p_2$
$p_2=3.4\times {10}^{4}Pa$