What restricts the water flow?

[eey01]

If I want to measure the flow at the bottom of a rain water pipe, then want to add a nozzle... how can I calculate the flow at the nozzle? will it be the same?

I have experimentally measured Q at the big pipe.

I want to design a Pelton turbine so I have to know how to calculate the flow and how the flow in affected as I decrease the area of the nozzle.

and how can I calculated the power of the system if the efficiency of the turbine is 80% and the height of the tube is 15ms.

will the jet velocity increase as we decrease the nozzle size? and if it increases to what limit...

thanks a lot!

 

[chrisbaird]

If I understand you right, you want Bernoulli's principle.

 

[Andy Resnick]

Adding a 'smooth' nozzle at the end of a pipe is a standard problem- I'm looking in Streeter's "Fluid Mechanics". From continuity, the flow velocities into (V_in) and out of (V_out) the nozzle are related by the two areas A_in and A_out:

V_out = (A_in/A_out)V_in

To get one of the velocities, you need to know the pressure at the nozzle inlet, as the pressure at the outlet is atmospheric. Most likely, you could set the pressure equal to the pressure required to generate the flow Q out of the open pipe. Then use Bernoulli's equation and you can solve for the velocities.

If the contraction is sudden, things are very different due to viscous effects. There will be a pressure drop within the nozzle ('minor losses') which depends on the ratio of the inlet and outlet diameters, the specific fluid,and the velocity at the inlet. If I did everything correctly, the pressure drop is

dP = (1/C -1)^2 V_out^2/(2*d), where 'C' is the 'contraction coefficient' and was first determined (for water) by Weisbach. 'd' is the density.

The advantage is that Bernoulli's equation can still be used- this head loss is simply another pressure term:

$P_{0} + \frac{V_{in}^{2}}{2ρ} = \frac{V_{out}^{2}}{2ρ} + dP =[1+(1/C-1)^{2}] \frac{V_{out}^{2}}{2ρ}$, and V_in and V_out are related by continuity as before.

Broadly speaking, decreasing the exit diameter will result in an increased velocity but decreased Q.

 

[eey01]

thank you :)

 

[PJC01]

I would first like to address what restricts the water flow in a rainwater pipe. There are several factors that can affect the flow of water in a pipe, including the diameter of the pipe, the material of the pipe, and any obstructions or bends in the pipe. These factors can create resistance and decrease the overall flow rate of the water.

To calculate the flow at the nozzle, you can use the continuity equation, which states that the flow rate at any point in a closed system must remain constant. This means that the flow rate at the bottom of the rainwater pipe should be the same as the flow rate at the nozzle, as long as there are no leaks or other factors affecting the flow.

To design a Pelton turbine, you will need to consider the flow rate and the velocity of the water jet. As the area of the nozzle decreases, the velocity of the water will increase according to the Bernoulli's principle. However, this increase in velocity will also result in a decrease in the flow rate, which will affect the overall power output of the system. To calculate the power of the system, you can use the equation P = Q x ρ x g x h x η, where Q is the flow rate, ρ is the density of the water, g is the acceleration due to gravity, h is the height of the tube, and η is the efficiency of the turbine.

The jet velocity will continue to increase as the nozzle size decreases, but there is a limit to this increase. At a certain point, the velocity will reach the speed of sound and cannot increase any further. This is known as the critical velocity. It is important to consider this limit when designing a Pelton turbine to ensure optimal efficiency and avoid damaging the turbine.

In summary, the flow rate and velocity of water in a pipe are affected by various factors such as pipe diameter, material, and obstructions. To calculate the flow at a nozzle, you can use the continuity equation. To design a Pelton turbine, you will need to consider the flow rate, velocity, and efficiency to determine the power output. It is also important to keep in mind the critical velocity limit when designing the turbine.