# Advice on pressure drop calculation

• DarkoX
In summary, to calculate the pressure drop across a pipe with the given parameters, you will need to calculate the relative roughness and nitrogen viscosity, and then use the Moody chart to find the friction factor. You will also need to find the equivalent length of one of the pipe's 90 degree bends and use the equation on the Moody chart to calculate the pressure drop. If the pressure drop is greater than 10%, you will need to divide the pipe into several lengths and calculate the pressure at the end of each length. Additionally, for a compressible ideal gas like N2, you will need to use the square of the pressure in your calculations.
DarkoX
TL;DR Summary
I am desperately need an advise/help on the calculation of pressure drop across the pipe.
Hello everyone,

I would appreciate any help with my task I am struggling to resolve. I need to calculate or simulate pressure drop when got the following parameters:

1. Supply pressure: 45barg.
2. Pipe Length: 80 meters
3. Pipe diameter: OD - 10mm, ID - 8mm.
4. Pipe material: stainless steel (SS316).
5. Pipe has 20 90deg bends distributed evenly across the pipe length.
6. Flow: well, it is bit more complicated as flow measured at 50 litres/min however after pressure is reduced from 45barg to 3.5barg (after pressure regulator).
7. Media: Pure N2 (nitrogen) gas.

How hard to calculate/simulate pressure drop across this pipe? Anyone can help me on this?

Much appreciated.

The Moody Chart (search the term) has everything you need to calculate the pressure drop. The chart in Wikipedia is a good one. You will need to do some calculations. Start as follows:

1) Calculate the relative roughness. If your pipe is drawn tubing, that would be 0.0025 / 8 = 3E-4.

2) Find the nitrogen viscosity. Here is a good source: https://www.engineeringtoolbox.com/air-absolute-kinematic-viscosity-d_601.html.

3) Calculate the Reynolds number. You will need to calculate or find the density, velocity, and viscosity of the nitrogen as it is flowing through the pipe. All of the inputs to the Reynolds number must be in consistent units so that the units will cancel. A properly calculated Reynolds number is dimensionless, and you need to confirm that the units cancel in order to verify your calculation.

4) Now that you have the Reynolds number and relative roughness, find the friction factor from the Moody chart. A screen shot of the Wikipedia Moody chart is shown below.

5) Find the equivalent length of one of the pipe 90 degree bends. Add to the actual length of the pipe, and use that total (actual plus equivalent) length for all pressure drop calculations. Use search term equivalent length pipe bend.

6) Use the equation on the Moody chart to find the pressure drop. If the pressure drop is less than about 10% of the inlet absolute pressure, you are done. If the pressure drop is greater than 10% (10% of 45 barg is 4.5 barg), divide the pipe into several lengths. Calculate the pressure at the end of the first length, use that as the input to the second length, etc.

Moody Chart:

You may be able find an online calculator, but it is a very good idea to verify by doing the calculation above.

BvU and Lnewqban
jrmichler said:
The Moody Chart (search the term) has everything you need to calculate the pressure drop. The chart in Wikipedia is a good one. You will need to do some calculations. Start as follows:

1) Calculate the relative roughness. If your pipe is drawn tubing, that would be 0.0025 / 8 = 3E-4.

2) Find the nitrogen viscosity. Here is a good source: https://www.engineeringtoolbox.com/air-absolute-kinematic-viscosity-d_601.html.

3) Calculate the Reynolds number. You will need to calculate or find the density, velocity, and viscosity of the nitrogen as it is flowing through the pipe. All of the inputs to the Reynolds number must be in consistent units so that the units will cancel. A properly calculated Reynolds number is dimensionless, and you need to confirm that the units cancel in order to verify your calculation.

4) Now that you have the Reynolds number and relative roughness, find the friction factor from the Moody chart. A screen shot of the Wikipedia Moody chart is shown below.

5) Find the equivalent length of one of the pipe 90 degree bends. Add to the actual length of the pipe, and use that total (actual plus equivalent) length for all pressure drop calculations. Use search term equivalent length pipe bend.

6) Use the equation on the Moody chart to find the pressure drop. If the pressure drop is less than about 10% of the inlet absolute pressure, you are done. If the pressure drop is greater than 10% (10% of 45 barg is 4.5 barg), divide the pipe into several lengths. Calculate the pressure at the end of the first length, use that as the input to the second length, etc.

Moody Chart:
View attachment 285474

You may be able find an online calculator, but it is a very good idea to verify by doing the calculation above.
One more thing. With N2 gas, the density will be changing. So we have $$\frac{dp}{dx}=-\frac{\rho v^2}{2d}f=-\frac{(\rho v)^2}{2\rho d}f=-(Re)^2\frac{\mu^2}{2\rho d^3}f$$with $$Re=\frac{4m}{\pi d \mu}$$where m is the mass flow rate. In addition, we have $$\rho=\frac{pM}{RT}$$This leads to $$\frac{dp^2}{dx}=-(Re)^2\left(\frac{RT}{M}\right)\frac{\mu^2}{d^3}f$$So, for a compressible ideal gas, we are working with the square of the pressure, rather than the pressure to the first power.

BvU

## 1. What is pressure drop and why is it important to calculate?

Pressure drop is the decrease in pressure that occurs as a fluid flows through a system. It is important to calculate because it affects the efficiency and performance of the system, and can also indicate potential problems such as blockages or leaks.

## 2. How is pressure drop calculated?

Pressure drop can be calculated using the Darcy-Weisbach equation, which takes into account factors such as fluid density, viscosity, flow rate, and pipe diameter. Other methods, such as the Hazen-Williams equation, may also be used depending on the specific system and fluid properties.

## 3. What factors can affect pressure drop?

Factors that can affect pressure drop include fluid properties (density, viscosity, etc.), flow rate, pipe diameter, pipe length and roughness, and fittings or obstructions in the system. Changes in these factors can result in changes in pressure drop.

## 4. How can pressure drop be minimized?

Pressure drop can be minimized by using larger pipe diameters, reducing the number of fittings and obstructions in the system, and using smoother pipe materials. Additionally, proper maintenance and regular cleaning of the system can help prevent blockages and reduce pressure drop.

## 5. What are some common mistakes to avoid when calculating pressure drop?

Common mistakes when calculating pressure drop include using incorrect fluid properties, not accounting for all components and obstructions in the system, and using outdated or inaccurate equations. It is important to double check all inputs and calculations to ensure accurate results.

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