Bernouli equation with pump work input

In summary, the conversation discusses using Bernoulli's equation to calculate the flow rate for a simple pump system. It is mentioned that the equation involves velocity, pressure, and elevation, and that the fluid velocity is assumed to be constant in the inlet pipe. The use of the nozzle diameter is questioned but it is unclear if it is relevant to the problem.
  • #1
boileroo
12
0

Homework Statement


Hey. I've posted a few questions around here lately, and really appreciate any help! thanks

Right, attached is an image showing a simple pump system.
Screenshot2011-05-22at160308.jpg


pump inlet gauge pressure = Pi = -34.2 kPa
nozzle diameter = 5cm
rho = 1000kg/m3

Calculate the flow rate

2. The attempt at a solution

I know that this is to be solved using a form of bernoulli's equation: [P1/rho * V12/2 + gz1] - [P2/rho * V22/2 + gz2] = work/mass flow rate.

I know that the velocity in the tank can be declared = 0, and the pressure at the nozzle outlet = Patm.

Any pointers please!
 
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  • #2
Do you have the Bernoulli's equation correct? According to the http://en.wikipedia.org/wiki/Bernoulli's_equation#Incompressible_flow_equation" it's
[tex]\frac{v^{2}}{2} + g z + \frac{p}{\rho} = constant[/tex]

You can write down the equation for two points in the inlet pipe where you know the pressures. But the fluid velocity in each of those points would be the same assuming the fluid is incompressible.

I don't see why you need the outlet nozzle diameter. Is this only one part of a larger problem?
 
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Related to Bernouli equation with pump work input

1. What is the Bernoulli equation with pump work input?

The Bernoulli equation with pump work input is a mathematical expression that describes the relationship between the pressure, velocity, and elevation of a fluid in a system. It takes into account the work done by a pump to increase the fluid's energy.

2. How is the Bernoulli equation with pump work input derived?

The Bernoulli equation with pump work input is derived from the principles of conservation of energy and the continuity equation. It is based on the concept that the total energy of a fluid in a system remains constant, and any changes in one form of energy (e.g. pressure) will result in a corresponding change in the other forms of energy (e.g. velocity and elevation).

3. What are the applications of the Bernoulli equation with pump work input?

The Bernoulli equation with pump work input has many practical applications in engineering and physics. It is commonly used in the design of pumps, turbines, and other fluid systems. It is also used in the analysis of fluid flow in pipes, nozzles, and other devices.

4. What are the assumptions made in the Bernoulli equation with pump work input?

The Bernoulli equation with pump work input makes several assumptions, including: the fluid is incompressible, the flow is steady, the flow is inviscid (no friction), and the pump work input is the only external work done on the fluid. These assumptions may not hold true in all real-world situations, but they allow for a simplified analysis of the fluid system.

5. How does the Bernoulli equation with pump work input relate to the concept of energy conservation?

The Bernoulli equation with pump work input is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another. In the context of fluid dynamics, this means that the total energy of the fluid remains constant as it moves through a system, even if there are changes in pressure, velocity, or elevation. The Bernoulli equation with pump work input helps to quantify these energy transformations and understand how they affect the behavior of the fluid.

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