How to find pressure in the system

[avinash.vijay]

Hello Everybady,

I have this situtation here. I have a liquid in a bowl rotating at a very high RPM creating a
a static pressure of 130-140 bars near the head. Now at the head of the bowl, I have a stationary centripetal pump attached which carries my liquid (driving force is the static pressure (or the rotational force) of liquid inside the bowl) through a pipe which leads to a vessel which is also pressurized.

I have some question which I am trying to find for the past one week but it just eats my brain when I try to find the solution for it.
The questions are,
1) How should I calculate the pressure at the entrance of the channel of my centripetal pump, and pressure also inside the channel.
2) the liquid is transferred to a vessel and the pressure inside the vessel ranges from atm pressure upto 10 bars.
3) to make sure my liquid from the rotating bowl reaches the receiving vessel, I should maintain the liquid pressure inside the trasfer pipe higher than that of my receiving vessel in order to avoid back pressure. am I right ?

'Since I am dealing with fluid dynamics after a very long time, I am not able to initiate the problem.

I tried Benoulli's principle, but since the driving force is due to the rotational force inside the bowl and not gravitational force, I am not able to use bernoullis theorem to calculate the static and dynamic pressure inside the centripetal pump.

A solution to this will be appreciated.

Thanks

 

[eljose79]

Thank you for sharing your intriguing situation with us. As a scientist with a background in fluid dynamics, I would be happy to provide some insights and suggestions to help you with your questions.

Firstly, to calculate the pressure at the entrance of the channel of your centripetal pump, you will need to consider the Bernoulli's principle along with the conservation of mass. The Bernoulli's principle states that the total energy of a fluid remains constant along a streamline. This means that the sum of static pressure, dynamic pressure, and potential energy remains constant at any given point. In your case, the potential energy can be neglected as it is not affected by the rotational force.

To calculate the pressure at the entrance of the channel, you can use the Bernoulli's equation, which is given by P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2, where P is the pressure, ρ is the density, v is the velocity, g is the gravitational acceleration, and h is the height. In this equation, P1 and P2 represent the pressure at the entrance and exit of the pump respectively, while v1 and v2 represent the velocities at those points. By rearranging the equation, you can solve for P1, which will give you the pressure at the entrance of the channel of your centripetal pump.

Similarly, to calculate the pressure inside the channel, you can use the same equation at different points inside the channel. You can assume that the velocity remains constant along the channel, and use the values of density and height at different points to calculate the pressure.

Regarding your second question, the pressure inside the vessel will depend on the depth of the liquid in the vessel. If the depth is significant, you will need to consider the hydrostatic pressure in addition to the atmospheric pressure. However, if the depth is small, you can consider the pressure to be equal to the atmospheric pressure.

Lastly, to ensure that the liquid from the rotating bowl reaches the receiving vessel, you are correct in assuming that the pressure inside the transfer pipe should be higher than the pressure inside the receiving vessel. This is to avoid any back pressure that may hinder the flow of the liquid.

I hope this helps you in your calculations and provides some clarity on your situation. If you have any further questions or need clarification on any of the points