Question

A steam pipe shown below has two sections, an expanded and contracted ends. The pressures, density, diameters and velocities of the pipe are given; fluid density ρ =960kg/m3 ,the sections diameters D1 = 100mm, D2=80mm, the gauge pressure at section one is P1 =200KN/m2 and the velocity at point one U1= 5m/s. What is the pressure at point 2?

Answer 1

$\frac{p_1}{\rho g}+\frac{u^2_1}{2 g}+z_1=\frac{p_2}{\rho g}+\frac{u^2_2}{2 g}+z_2\\ z_1=z_2\\ p_2=p_1+\frac{\rho}{2}(u_1^2-u_2^2)\\$

Use the continuity equation to find u₂

$A_1u_1=A_2u_2\\ u_2= \frac{A_1u_1}{A_2}= \frac{d^2_1}{d^2_2}u_1\\ = 7.8125 m/s$

So pressure at section 2

$p_2= 200000-17296.87\\ =182703 N/m^2$