Prashant Kumar Sharma
I have this conceptual problem which I asked many people regarding pressure velocity problem and many got confused, I later turned this problem into pressure velocity paradox.Please help me with this problem:
Suppose you take a pipe of uniform cross-section with which has got lots of bends( the setup in on a horizontal table). Now, water flows in and due to lots of bends there would be head losses and so, the pressure at the inlet would not be same as at the exit.
Now the problem is, if we apply continuity equation A1V1=A2V2 and the inlet and exit then the velocity must be same( since the area is same throughout).
But according to Bernoulli, change in pressure energy is equal to change in kinetic energy, and since the pressure has changed so should the velocity at different points.
These two points are contradicting. Could you please help?
If the fluid flow is steady and the liquid is incompressible, then ideally,
A1V1=A2V2, it will hold true.
Now as far as Bernoulli's equation, change of pressure energy will not be there if bend is smooth ( and cross sectional area doesnot changes).
In case of steep bends, pressure will change but cross sectional area at that point will also change, thus A2 will also change, compensating for change in velocity.
Think of it as in this way, if pipe is full of water, and u start pushing 200 ml of water each second, 200 ml of water will come out each second (as water cannot disappear in between).
I am no expert in this field, but I go with common experience that I have of physical phenomenon😀