Understanding Bernoulli's Equation for Fluid Dynamics with Electric Pumps

[mattyboson12]

Hi, am having a few problems applying bernoulli's equation when an electric pump is involved. I have attached a picture of the question. I understand how to apply bernoullis for venturi and pitot tubes but when it involves work being done on the system eg. a water pump, fan exhaust I don't know where to start.

 

[paisiello2]

Can you attempt to answer part a)?

 

[mattyboson12]

Thank you for the reply. This is my answer but I'm not sure if its right as I am getting a negative value for the pump power?

 

[paisiello2]

For part b), you assumed that the difference between the energies at point 1 and 5 is equal to the Work done by the pump. This is correct except the Work is effectively being added to the system at point 1. You incorrectly assumed it is being subtracted from point 1 (or equivalently that it was being added at point 5).

The water coming out at point 5 doesn't really know if there was a pump or if the water level was much higher than that as shown at point 1. So all the energy terms should be additive at point 1 and be set equal to the energy terms at point 5.

 

[rezeew]

Hello,

Thank you for your question. Bernoulli's equation is a fundamental equation in fluid dynamics that relates the pressure, velocity, and height of a fluid in a system. It is commonly used to analyze the flow of fluids in pipes, pumps, and other systems.

When an electric pump is involved, the equation can still be applied, but there are some additional factors to consider. First, the pump itself will add energy to the system, increasing the velocity and potentially changing the pressure of the fluid. This added energy will need to be accounted for in the equation.

Additionally, the pump will also have an impact on the overall flow rate and pressure of the fluid in the system. Therefore, it is important to consider the pump's characteristics, such as its flow rate and head, when applying Bernoulli's equation.

One approach to solving problems involving electric pumps and Bernoulli's equation is to break the system into smaller sections and analyze each section separately. This will allow you to account for the changes in pressure and velocity caused by the pump at each section.

In terms of the specific problem you have attached, it may be helpful to first identify the different sections of the system and then apply Bernoulli's equation to each section, taking into account the work done by the pump. It may also be useful to consider the conservation of energy in the system, as the pump will be adding energy to the fluid.

I hope this helps. If you have any further questions, please don't hesitate to ask. Wishing you success in your studies of fluid dynamics.

Best,