An abrupt contraction is geometrically the reverse of an abrupt enlargement . Here also the streamlines cannot follow the abrupt change of geometry and hence gradually converge from an upstream section of the larger tube.
However, immediately downstream of the junction of area contraction, the cross-sectional area of the stream tube becomes the minimum and less than that of the smaller pipe. This section of the stream tube is known as vena contracta, after which the stream widens again to fill the pipe.
The velocity of flow in the converging part of the stream tube from Sec. 1-1 to Sec. c-c (vena contracta) increases due to continuity and the pressure decreases in the direction of flow accordingly in compliance with the Bernoulli’s theorem.
In an accelerating flow,under a favourable pressure gradient, losses due to separation cannot take place. But in the decelerating part of the flow from Sec. c-c to Sec. 2-2, where the stream tube expands to fill the pipe, losses take place in the similar fashion as occur in case of a sudden geometrical enlargement. Hence eddies are formed between the vena contracta c-c and the downstream Sec. 2-2.
The flow pattern after the vena contracta is similar to that after an abrupt enlargement, and the loss of head is thus confined between Sec. c-c to Sec. 2-2. Therefore, we can say that the losses due to contraction is not for the contraction itself, but due to the expansion followed by the contraction.
Consider a liquid flowing through in a pipe which has a sudden contraction in area. Consider two sections 1-1 and 2-2 before and after contraction. As the liquid flows from large pipe to smaller pipe, the area of flow goes on decreasing and becomes minimum at a section C-C. This section C-C is called Vena-contracta. After section C-C, a sudden enlargement of the area takes place. The loss of head due to sudden contraction is actually due to sudden enlargement from Vena-contracta to smaller pipe.
Let,
Ac = Area of flow at section C-C
Vc = Velocity of flow at section C-C
A2 = Area of flow at section 2-2
hc = Loss of head due to sudden contraction
Now hc = actual loss of head due to enlargement from section C-C to section 2-2 and is given
Credit:- https://nptel.ac.in/courses/112104118/lecture-14/14-7_losses_sudden_contract.htm
However, immediately downstream of the junction of area contraction, the cross-sectional area of the stream tube becomes the minimum and less than that of the smaller pipe. This section of the stream tube is known as vena contracta, after which the stream widens again to fill the pipe.
The velocity of flow in the converging part of the stream tube from Sec. 1-1 to Sec. c-c (vena contracta) increases due to continuity and the pressure decreases in the direction of flow accordingly in compliance with the Bernoulli’s theorem.
In an accelerating flow,under a favourable pressure gradient, losses due to separation cannot take place. But in the decelerating part of the flow from Sec. c-c to Sec. 2-2, where the stream tube expands to fill the pipe, losses take place in the similar fashion as occur in case of a sudden geometrical enlargement. Hence eddies are formed between the vena contracta c-c and the downstream Sec. 2-2.
The flow pattern after the vena contracta is similar to that after an abrupt enlargement, and the loss of head is thus confined between Sec. c-c to Sec. 2-2. Therefore, we can say that the losses due to contraction is not for the contraction itself, but due to the expansion followed by the contraction.
Consider a liquid flowing through in a pipe which has a sudden contraction in area. Consider two sections 1-1 and 2-2 before and after contraction. As the liquid flows from large pipe to smaller pipe, the area of flow goes on decreasing and becomes minimum at a section C-C. This section C-C is called Vena-contracta. After section C-C, a sudden enlargement of the area takes place. The loss of head due to sudden contraction is actually due to sudden enlargement from Vena-contracta to smaller pipe.
Let,
Ac = Area of flow at section C-C
Vc = Velocity of flow at section C-C
A2 = Area of flow at section 2-2
hc = Loss of head due to sudden contraction
Now hc = actual loss of head due to enlargement from section C-C to section 2-2 and is given
Credit:- https://nptel.ac.in/courses/112104118/lecture-14/14-7_losses_sudden_contract.htm
- Book Author- DR.R.K.Bansal
Comments
Post a Comment