Loss due to sudden enlargement
If the cross-section of a pipe with fluid flowing through it, is abruptly enlarged at certain place, fluid emerging from the smaller pipe is unable to follow the abrupt deviation of the boundary.
The streamline takes a typical diverging pattern. This creates pockets of turbulent eddies in the corners resulting in the dissipation of mechanical energy into intermolecular energy.
Basic mechanism of this type of loss
The fluid flows against an adverse pressure gradient. The upstream pressure p1 at section a-b is lower than the downstream pressure p2 at section e-f since the upstream velocity V1 is higher than the downstream velocity V2 as a consequence of continuity.
The fluid particles near the wall due to their low kinetic energy cannot overcome the adverse pressure hill in the direction of flow and hence follow up the reverse path under the favourable pressure gradient (from p2 to p1).
This creates a zone of recirculating flow with turbulent eddies near the wall of the larger tube at the abrupt change of cross-section, resulting in a loss of total mechanical energy.
For high values of Reynolds number, usually found in practice, the velocity in the smaller pipe may be assumed sensibly uniform over the crosssection. Due to the vigorous mixing caused by the turbulence, the velocity becomes again uniform at a far downstream section e-f from the enlargement (approximately 8 times the larger diameter).
Consider a liquid flowing through a pipe which has sudden enlargement. 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 section 2-2.
Due to sudden change of diameter of the pipe from D1 to D2, the liquid flowing from the smallest pipe is not able to follow the abrupt change of the boundary. Thus the flow separates from the boundary and turbulent eddies are formed. The loss of head ( or energy) takes place due to the formation of these eddies.
Let
p' = pressure intensity of the liquid eddies on the area ( A2 - A1 )
Applying Bernoulli's equation at sections 1-1 and 2-2
Consider the control volume of liquid between sections 1-1 and 2-2. Then the force acting on the liquid in the control volume in the direction of flow is given by
Now net force acting on the control volume in the direction of flow must be equal to the rate of change of momentum or change of momentum per second.
Credit:- https://nptel.ac.in/courses/112104118/lecture-14/14-6_losses_sudden_enlarg.htm
Book Author- Dr.R.K.Bansal
If the cross-section of a pipe with fluid flowing through it, is abruptly enlarged at certain place, fluid emerging from the smaller pipe is unable to follow the abrupt deviation of the boundary.
The streamline takes a typical diverging pattern. This creates pockets of turbulent eddies in the corners resulting in the dissipation of mechanical energy into intermolecular energy.
Basic mechanism of this type of loss
The fluid flows against an adverse pressure gradient. The upstream pressure p1 at section a-b is lower than the downstream pressure p2 at section e-f since the upstream velocity V1 is higher than the downstream velocity V2 as a consequence of continuity.
The fluid particles near the wall due to their low kinetic energy cannot overcome the adverse pressure hill in the direction of flow and hence follow up the reverse path under the favourable pressure gradient (from p2 to p1).
This creates a zone of recirculating flow with turbulent eddies near the wall of the larger tube at the abrupt change of cross-section, resulting in a loss of total mechanical energy.
For high values of Reynolds number, usually found in practice, the velocity in the smaller pipe may be assumed sensibly uniform over the crosssection. Due to the vigorous mixing caused by the turbulence, the velocity becomes again uniform at a far downstream section e-f from the enlargement (approximately 8 times the larger diameter).
Consider a liquid flowing through a pipe which has sudden enlargement. 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 section 2-2.
Due to sudden change of diameter of the pipe from D1 to D2, the liquid flowing from the smallest pipe is not able to follow the abrupt change of the boundary. Thus the flow separates from the boundary and turbulent eddies are formed. The loss of head ( or energy) takes place due to the formation of these eddies.
Let
p' = pressure intensity of the liquid eddies on the area ( A2 - A1 )
Applying Bernoulli's equation at sections 1-1 and 2-2
Consider the control volume of liquid between sections 1-1 and 2-2. Then the force acting on the liquid in the control volume in the direction of flow is given by
Credit:- https://nptel.ac.in/courses/112104118/lecture-14/14-6_losses_sudden_enlarg.htm
Book Author- Dr.R.K.Bansal
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