Question

Is it possible to have a pressure increase in spite of the head loss caused by the sudden expansion?

Answer 1

Answer:

Yes it is possible for the pressure to increase if head loss occurs in a pipe due to sudden enlargement.

Explanation: Consider the attached figure

The head loss in a pipe due to sudden enlargement is given by

$h_L=(\frac{V_{1}^{2}-V_{2}^{2}}{2g})$

where $V_1$ is the velocity in the smaller pipe

$V_2$ is the velocity in the larger pipe

Now by Bernoulli's theorm between the 2 points in the pipe we have

$\frac{p_{2}-p_1}{\rho }=\frac{v_{1}^{2}-v_{2}^{2}}{2}-gh_L$

In the above equation we can see that

for $v_1> v_2$ we have $p_2> p_1$

thus pressure increases