Question

Use the conservation of linear momentum principle to derive one of the following:

a. The head loss formula for a hydraulic jump

b. The minor loss coefficient for a sudden pipe contraction

Answer 1

Consider a flow as shown in figure below.

There is a sudden contraction that furthe leads to a vena-contracta where Vc and Ac are the velocity and cross sectional area respectively.

A1, V1 and A2,V2 are the area and velocity at section 1 and 2 respectively.

where Pc is pressure at section c

Vc velocity at section c

P2 pressure at section 2

V2 velocity at section 2

hL is head loss. { Its assumed that the entire loss occurs at vena contracta and not between section 1 and c}

rho is mass density of fluid

g is acceleration due to gravity

The term in square brackets is called minor loss coefficient of sudden contraction in pipe.

hL = head loss= K(V2)²/2g

K= minor head loss coefficient=[1/Cc-1]²

where Cc is coefficient of contraction=Ac/A2