Question

Question:An ideal fluid flows through a horizontal pipe whose diameter varies along its length. Measurements would indicate that the sum of the kinetic energy per unit volume and pressure at different sections of the pipe would (a) decrease as the pipe diameter increases, (b) increase as the pipe diameter increases, (c) increase as the pipe diameter decreases, (d) decrease as the pipe diameter decreases, or (e) remain the same as the pipe diameter changes.

Short answer

Pressure at different sections of the pipe would remain the same as the pipe diameter changes. Hence the correct answer is option (e).

Step-by-step solution

Step 1: Bernoulli’s equation

The sum of the pressure, kinetic energy per unit volume, and gravitational potential energy per unit volume has the same value at all points along a streamline for an ideal fluid. This result is summarized in Bernoulli’s equation:

P+$\frac{1}{2}\rho V^2+\rho gy=cons\tan t$

Where

P=Pressure of fluid

V=Volume of fluid

$\rho =$Density of fluid

h=Height of fluid in pipe

Find the correct answer

• AccordingtoconceptBernoulli’ssaysthatthetotalenergyremainsconstant.Assumingthepipeliesonahorizontalleveledgroundandthereisnoexchangeofenergy.
• Thesumofkineticenergyandpressureatdifferentsectionofthepipewouldremainsameasthediameterofthepipechanges.
• Hence the correct answer is option (e).