Solving Orifice Plate Calculation Equation - Help Needed

  • Thread starter mattaddis
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In summary, the conversation discusses a mechanical engineer seeking help with building an Excel document for orifice plate calculations. The engineer is specifically stuck on solving an equation for d2 and receives assistance from another user. Two different formulas are provided and one is determined to be correct based on testing. The engineer expresses gratitude for the assistance.
  • #1
mattaddis
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Hello there,

I am a mechanical engineer and am attempting to build an Excel document for calculations purposes.

Currently I am stuck on orifice plate calculations.

I was wondering if someone could help me solve the following equation for d2?

[tex]\alpha[/tex] = [tex]\pi[/tex](d2/2)2 [tex]\sqrt{}[/tex]1/1-(d2/d1)4

Any help would be appreciated.

Thanks in advance.

(Apologies if I have posted this in the wrong place)

Matt
 
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  • #2
Sure thing,

[tex]\alpha = \pi\left(\frac{d_2}{2}\right)^2\sqrt{\frac{1}{1-\left(\frac{d_2}{d_1}\right)^4}}[/tex]

square the entire equation to rid yourself of the square root:

[tex]\alpha^2 = \pi^2\left(\frac{d_2}{2}\right)^4\left(\frac{1}{1-\left(\frac{d_2}{d_1}\right)^4}\right)[/tex]

Multiply through by that denominator:

[tex]\alpha^2\left(1-\left(\frac{d_2}{d_1}\right)^4}\right) = \pi^2\left(\frac{d_2}{2}\right)^4[/tex]

Expand the left side, and move the right to the left side:

[tex]\alpha^2-\alpha^2\left(\frac{d_2}{d_1}\right)^4} -\pi^2\left(\frac{d_2}{2}\right)^4=0[/tex]

This can be more easily visualized as:

[tex]\alpha^2-d_2^4\frac{\alpha^2}{d_1^4} -d_2^4\frac{\pi^2}{16}=0[/tex]

Factorize out the required variable:

[tex]\alpha^2-d_2^4\left(\frac{\alpha^2}{d_1^4} +\frac{\pi^2}{16}\right)=0[/tex]

Well you can probably finish it from here, and you might want to manipulate some things so you don't have fractions in fractions.
 
  • #3
Check if it's
[tex]d_2=\frac{1}{\sqrt[4]{\left(\frac{\pi}{4\alpha}\right)^2+\frac{1}{d_1^4}}}[/tex]
 
  • #4
Thankyou both for yor prompt reply.

I have tested the two formulas based on existing figures and Mentallic's formula/equation gives the desired result.

Gerenuk, you equation gives d1, not d2.

Thank you very much for your assistance.

Matt
 
  • #5
You're welcome :smile:
 

1. What is an orifice plate calculation equation?

An orifice plate calculation equation is a formula used to determine the flow rate of a fluid through an orifice plate, which is a device used to measure and control the flow of a fluid. It takes into account factors such as the size and shape of the orifice, the fluid properties, and the pressure differentials.

2. Why is it important to solve the orifice plate calculation equation?

Solving the orifice plate calculation equation is important in order to accurately measure and control the flow of a fluid. This is crucial in many industries, such as oil and gas, chemical, and water treatment, where precise flow measurements are necessary for process control and optimization.

3. What are the variables included in the orifice plate calculation equation?

The variables included in the orifice plate calculation equation may vary depending on the specific equation being used, but generally they include the orifice diameter, fluid density and viscosity, upstream and downstream pressures, and the discharge coefficient of the orifice plate.

4. How do I solve the orifice plate calculation equation?

Solving the orifice plate calculation equation involves plugging in the values of the variables into the equation and solving for the unknown variable (usually the flow rate). It is important to use consistent units for all variables and to ensure accurate measurements to get an accurate result.

5. Are there any common mistakes when solving the orifice plate calculation equation?

Yes, there are a few common mistakes that can occur when solving the orifice plate calculation equation. These include using incorrect units, not accounting for all necessary variables, and not using the correct equation for the specific type of orifice plate being used. It is important to double check all inputs and calculations to ensure an accurate result.

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