Question

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

Answer 1

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=((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

`(p_(2)-p_1)/(\rho )=(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