Question

A horizontal pipeline carries water in a streamline flow. The inlet area of the pipeline is $40{\text{cm}}^2\&$ water velocity at inlet is $1\text{m/s}$. Find the pressure at the outlet of pipeline if the inlet pressure is $4000\text{Pa}$ and outlet cross-section is $20{\text{cm}}^2$. Will the result for outlet pressure be same, if we place a heater inside the pipeline assuming the walls of the pipeline to be insulated. Take ${\rho }_{H_{2}O}=1000{\text{kg/m}}^3$.

• A. $2000\text{Pa}$, No pressure will not be same
• B. $3500\text{Pa}$, Yes pressure will be same
• C. $2500\text{Pa}$, No pressure will not be same
• D. $2000\text{Pa}$, Yes pressure will be same

Answer 1

The correct option is C $2500\text{Pa}$, No pressure will not be same


Using equation of continuity at cross-section $1\&2$
$A_1{V}_1=A_2{V}_2$
$\Rightarrow 40\times 1=20\times V_2$
$\Rightarrow V_2=2\text{m/s}$

Now, applying Bernoulli's theorem
$P_1+\frac{1}{2}\rho v_1^2=P_2+\frac{1}{2}\rho v_2^2$
$\Rightarrow 4000+\frac{1}{2}\times 1000\times 1^2=P_2+\frac{1}{2}\times 1000\times 2^2$
$\Rightarrow P_2=4500-2000$
$=2500\text{Pa}$

If a heater is placed inside the pipeline, the thermal energy added to water will manifest itself in terms of increased pressure at outlet.