Calculating Mass Flow Rate: Pump Water Through Nozzle

In summary, the conversation discusses a pump delivering water through a hose with a nozzle and the pressure, temperature, and power input required. The task is to determine the mass flow rate delivered by the pump. Equations mentioned include m_dot (deltaPE) = W and m_dot = rho*Volumetric flow rate, but no clear solution is found.
  • #1
Colts
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Homework Statement


A pump steadily delivers water through a hose terminated
by a nozzle. The exit of the nozzle has a diameter of 0.6 cm
and is located 10 m above the pump inlet pipe, which has a
diameter of 1.2 cm. The pressure is equal to 1 bar at both the
inlet and the exit, and the temperature is constant at 20° C. The
magnitude of the power input required by the pump is 1.5 kW,
and the acceleration of gravity is g = 9.81 m/s^2. Determine
the mass flow rate delivered by the pump, in kg/s.


Homework Equations


Not sure. I think
m_dot (deltaPE) = W

I don't know if I can use the work by the pump though.
m_dot = rho*Volumetric flow rate

The Attempt at a Solution


Well these are the only equations I can think of and I'm not sure if these are right. Any help where to go form here would be appreciated.
 
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  • #2
Someone else pitch in! I get an unwieldy third-order polynomial!
 
Last edited:

1. What is mass flow rate and why is it important?

Mass flow rate is the measurement of how much mass is passing through a given point per unit of time. In the context of pumping water through a nozzle, it is the amount of water that is flowing through the nozzle per unit of time. It is an important measurement because it helps determine the efficiency of the pump and the amount of water that can be delivered to a specific location.

2. How do you calculate mass flow rate?

To calculate mass flow rate, you need to know the density of the fluid (water in this case), the velocity of the fluid, and the cross-sectional area of the nozzle. The formula for mass flow rate is mass flow rate = density x velocity x cross-sectional area. This can be further simplified to Q = ρ x V x A, where Q is the mass flow rate, ρ is the density, V is the velocity, and A is the cross-sectional area.

3. What factors can affect the mass flow rate when pumping water through a nozzle?

The main factors that can affect the mass flow rate when pumping water through a nozzle are the size and shape of the nozzle, the pressure and velocity of the water, and the viscosity of the fluid. Additionally, any obstructions or restrictions in the flow path can also affect the mass flow rate.

4. How can I increase the mass flow rate when pumping water through a nozzle?

To increase the mass flow rate when pumping water through a nozzle, you can either increase the pressure or the velocity of the water. This can be achieved by using a more powerful pump, increasing the diameter of the nozzle, or decreasing any restrictions in the flow path.

5. How does the mass flow rate affect the efficiency of a pump?

The mass flow rate directly affects the efficiency of a pump. A higher mass flow rate means the pump is delivering more water in a given amount of time, which indicates a more efficient pump. However, if the mass flow rate is too high, it can also lead to inefficiencies such as cavitation, which can damage the pump and decrease its efficiency. It is important to find the optimal mass flow rate for the specific pump and application.

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