Head loss due to a sudden enlargement in a pipe is

Explanation:

There are generally two types of losses

• Minor losses
• Major losses

Minor losses: Whenever there is a change in the cross-section, minor losses occur.

For e.g. sudden expansion, sudden contraction or bend in the pipes.

Major losses: Whenever the losses in the pipes are because of friction they are considered as major losses because there is significant loss of energy because of friction.

According to Darcy’s Weisbach equation:

1. Major loss (hL): this is the head loss due to friction.

• \({h_L} = \frac{{fL{V^2}}}{{2gD}}\)

where f = friction factor, L = length of pipe, V = velocity of flow, D = diameter of the pipe

2. Minor losses:

Sudden expansion loss:

Sudden Expansion:

The value of k depends on the angle of the bend and the radius of the curvature of the bend.

Loss of Head Due to Sudden Enlargement. Consider a liquid flowing through a pipe that has sudden enlargement as shown in Fig. Consider two sections (1)-(1) and (2)-(2) before and after the enlargement.

Let p1 = pressure intensity at section 1-1,

V1 = velocity of flow at section 1-1,

A1 = area of pipe at section 1-1,

p2, V2, and A2 = corresponding values at sections 2-2.

Due to the sudden change of diameter of the pipe from D1 to D2, the liquid flowing from the smaller pipe is not able to follow the abrupt change of the boundary. Thus the flow separates from the boundary and turbulent eddies are formed as shown in Fig. The loss of head (or energy) takes place due to the formation of these eddies.

Sudden expansion loss:

\({\left( {{h_L}} \right)_{exp}} = \frac{{{{\left( {{v_1} - {v_2}} \right)}^2}}}{{2g}}\)​Exit loss:\({\left( {{h_L}} \right)_{exit}} = \frac{{v_1^2}}{{2g}}\)

Sudden contraction loss:

• \({\left( {{h_L}} \right)_{con}} = \frac{{{{\left( {{v_c} - {v_2}} \right)}^2}}}{{2g}}\)

where vc = velocity at vena contracta

Entrance loss:

• \({\left( {{h_L}} \right)_{ent}} = \frac{{0.5 \times v_2^2}}{{2g}}\)

Bend loss:

• \({\left( {{h_L}} \right)_{bend}} = \frac{{k{v^2}}}{{2g}}\)