Calculating pump pressures and power (Bernouilli)

• Xengine
In summary: Pa (i assumed h_A to be equal to 0, not sure if this is correct)outlet: using the previous value as p1 now, assuming v1=v2 and z1=0 and z2=12.2m i found a p2 of 107.71 kPapower: 0.057*1000*9.81*15.25 = 8.53kW
Xengine

Homework Statement

http://imgur.com/ktfgCAL

flow rate: 0.057 m^3/s
cross sectional area of all pipes: 1.864*10^-2 m²
frictional losses inlet pipe: 1.83m
frictional losses outlet pipe: 3.66m
density: 1000 kg/m^3
g= 9.81 N/kg

pressure at inlet
pressure at outlet
necessary pumping power

Homework Equations

Bernouilli: http://imgur.com/EEptkNX where h_A is the energy added by the pump and h_r and h_l are the losses
pumping power= q*rho*g*h

The Attempt at a Solution

first of all, i am not sure what location they actually mean exactly by pump inlet and outlet (is it in the tank or really at the pump?)

inlet: I assumed p1 to be 0, v1=v2 and z1=0 and z2=3.05m which results in a p2 of 47.87kPa (i assumed h_A to be equal to 0, not sure if this is correct)
outlet: using the previous value as p1 now, assuming v1=v2 and z1=0 and z2=12.2m i found a p2 of 107.71 kPa
power: 0.057*1000*9.81*15.25 = 8.53kW

Apparentely, all my answers seem to be wrong. I'm fairly sure that I am making a critical mistake for the pressure calculations, but I really don't understand what could be wrong in my power calculation.

Last edited:
Xengine said:

Homework Statement

http://imgur.com/ktfgCAL

flow rate: 0.057 m^3/s
cross sectional area of all pipes: 1.864*10^-2 m²
frictional losses inlet pipe: 1.83m
frictional losses outlet pipe: 3.66m

pressure at inlet
pressure at outlet
necessary pumping power

Homework Equations

Bernouilli: http://imgur.com/EEptkNX where h_A is the energy added by the pump and h_r and h_l are the losses
pumping power= q*rho*g*h

The Attempt at a Solution

first of all, i am not sure what location they actually mean exactly by pump inlet and outlet (is it in the tank or really at the pump?)

The pump inlet and outlet seem to be indicated pretty clearly on the system diagram. The pump outlet is located further away from the pump itself apparently to accommodate the shut-off valve.

SteamKing said:
The pump inlet and outlet seem to be indicated pretty clearly on the system diagram. The pump outlet is located further away from the pump itself apparently to accommodate the shut-off valve.

But there isn't any data given about the exact height of the outlet point for example, i think the arrow just indicates the inlet and outlet pipe rather than the specific point that the pressure needs to be calculated on, or am I missing something?

1. How do you calculate pump pressure using Bernouilli's equation?

To calculate pump pressure using Bernouilli's equation, you need to know the fluid velocity, density, and elevation change of the fluid. The equation is P + (1/2)(density)(velocity)^2 + density(acceleration due to gravity)(height) = constant. You can rearrange the equation to solve for pressure, which is represented by P.

2. What factors affect pump pressure and power?

The main factors that affect pump pressure and power are the flow rate, fluid density, fluid viscosity, and the head (elevation change) of the fluid. The type and design of the pump can also play a role in determining the pressure and power required.

3. How do you calculate the power of a pump?

The power of a pump can be calculated by multiplying the flow rate (in cubic feet per second) by the head (in feet) and dividing by the pump efficiency. The equation is P = (Q x H) / η, where P is power, Q is flow rate, H is head, and η is efficiency.

4. What is the relationship between pump pressure and power?

Pump pressure and power are directly related. As pump pressure increases, the power required to generate that pressure also increases. This is because a higher pressure means more work is needed to move the fluid against resistance, resulting in a higher power requirement for the pump.

5. How can you determine the maximum pressure a pump can produce?

The maximum pressure a pump can produce is determined by the design and capabilities of the pump. You can refer to the pump's specifications or consult with the manufacturer to determine its maximum pressure capacity. It is important to also consider the fluid properties and any potential constraints, such as the available power supply, to ensure the pump can operate at its maximum pressure without any issues.

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