Calculating the force from a pump + nozzle system

[CCM_CAN]

I am attempting to calculate the force (in KgF) of a water pump + nozzle system. I have the pump curve (head vs. flow rate) for the pump, the diameter of the connection hose (2 inches) and the nozzle diameter (1 inch). The connection hose between the pump and nozzle is very short (approx 10 cm). How do I calculate the possible forces created by this system by tuning the flow rate output from the pump? Thanks!

Example point on the pump curve: 20 psi at 180 gallons per minute.

 

[berkeman]

Welcome to the PF.

Which force on what where? The force of the stream of fluid on something at some distance away from the nozzle? Or some other force? Sorry, but it's not obvious to me from reading your question. Thanks.

 

[CCM_CAN]

The propulsive force of the water stream coming out of the nozzle. Basically I am trying to combine the pump characteristics and curve with the analysis given on the following link: https://www.engineeringtoolbox.com/jet-discharge-propulsion-force-d_1868.html

The area I am unsure of is how to use the analysis from the link above with what I know about the pump (pump curve).

 

[Dullard]

You posted in 'Engineering' rather than 'Physics,' so:

You can safely ignore the 2" hose - any contribution from it will disappear in other non-idealities.

You have to determine where on the pump curve that you'll be operating. That is the point where the pump curve intersects with the 'system curve.' This may be done mathematically or graphically - I'd do it graphically. Absent other information, you can approximate the Cv for a 1" (ID) nozzle at 27. The nozzle curve (that you generate from the Cv) is your system curve. Once you determine that point, you'll know the flow and pressure at the nozzle inlet.

You mention 'tuning' the flow rate. If that's by means of pump speed control, you'll need to generate a new pump curve for each speed and determine the new intersection point; if by means of a 'throttle valve' between the pump and nozzle, you'll need to add the flow characteristics of the valve to your nozzle characteristics to get the system curve.

Assuming that you were using a small (or long) hose, the characteristics of that might also need to be included in your system curve.

 

[russ_watters]

I am attempting to calculate the force (in KgF) of a water pump + nozzle system. I have the pump curve (head vs. flow rate) for the pump, the diameter of the connection hose (2 inches) and the nozzle diameter (1 inch). The connection hose between the pump and nozzle is very short (approx 10 cm). How do I calculate the possible forces created by this system by tuning the flow rate output from the pump? Thanks!

Example point on the pump curve: 20 psi at 180 gallons per minute.

Do you have a performance curve for the nozzle, or is it just a simple cone?

 

[CCM_CAN]

Simple cone, linear decrease in diameter from 2 inch to `1 inch.

 

[russ_watters]

Simple cone, linear decrease in diameter from 2 inch to `1 inch.

@Dullard gave a good method just before I posted my question. Cv is called a flow coefficient. you can google for the equation, graph it, and see where it intersects the pump curve to get your flow rate.

Alternately and separately I was plugging values into an orifice flow rate calculator on tlv.com and using a 90% efficiency/discharge coefficient yields the same 27 Cv. You could plug in different values for pressure drop until you hit a point on your curve. It's actually not too far off the point you picked as your sample.