Calculating the suction force produced by a Venturi

[amrbekhit]

Dear all,

As I understand the venturi effect, if a flow of water passes through a constriction, its velocity increases and its pressure decreases at the restriction. The decrease in pressure allows a suction force to be produced.

I am trying to use this principle in order to power a vacuum cup inside a water pipe, but my initial calculations for estimating the suction force are producing seemingly meaningless results.

According to http://www.wolframalpha.com/input/?i=venturi", the formula describing the venturi effect is:

[tex]Q=1/4\,\pi\,{{\it D1}}^{2}\sqrt {2}\sqrt {{\frac {{\it P1}-{\it P2}}{
\rho}}}{\frac {1}{\sqrt {{\frac {{{\it D1}}^{4}}{{{\it D2}}^{4}}}-1}}}
[/tex]

From my understanding, the vacuum pressure generated by the venturi is [tex]P1-P2[/tex]. So, rearranging the above equation to make that the subject gives:

[tex]{\it P1}-{\it P2}=8\,{Q}^{2} \left( {\frac {{{\it D1}}^{4}}{{{\it D2}}
^{4}}}-1 \right) \rho{\pi }^{-2}{{\it D1}}^{-4}[/tex]

In my situation, I have the following known information:

• Diameter of pipe: 8"
• Water speed: 0.9m/s
• Water Pressure: 2.8bar

From the diameter and water speed, I calculate that the flow rate is:

[tex]0.02919\,{\frac {{m}^{3}}{s}}[/tex]

Other information that is required:

• Venturi upstream diameter D1: 10e-3 m
• Venturi downstream diameter D2: 5e-3 m
• Density of water rho: 1000kg/m^3

Substituting all of that information into the formula gives us a pressure difference of 1.035716981*10^9 Pa (which looks huge).

Assuming that my suction cup has a 15mm radius, in order to work out the suction force I use:

[tex]F=PA[/tex]

This gives me a suction force of 732105N!

This seems extremely high to me, which makes me think that I have misunderstood the principle. Can anyone shed some light on this?

Thanks

--Amr

 

[amrbekhit]

Any thoughts?

 

[charng]

Hello Amr,

Thank you for sharing your calculations and concerns about using the Venturi effect to create suction in a water pipe. It seems like you have a good understanding of the principle and have done a thorough job in your calculations. However, I can understand why the results may seem confusing or too high.

Firstly, I would like to clarify that the formula you have used is correct and is commonly used to calculate the pressure difference created by a Venturi. However, it is important to note that this formula assumes an ideal, frictionless flow. In real-life situations, there will always be some loss of energy due to friction and other factors, which can affect the accuracy of the calculations. Additionally, the formula does not take into account the shape and size of the suction cup, which can also affect the actual suction force produced.

Furthermore, the pressure difference calculated using the formula is the maximum possible pressure difference that can be created by a Venturi. In reality, the actual pressure difference will be lower due to energy losses. This could explain why your calculated suction force seems too high.

I would suggest conducting some experiments to test the effectiveness of using a Venturi to create suction in a water pipe. This will give you a more accurate understanding of the results and help you make any necessary adjustments to your calculations.

I hope this helps clarify your concerns. Keep up the good work in your research!