# Scaling pressure drop to other temperatures

• freddie_mclair
In summary, if you want to extrapolate pressure drop data between temperatures, you can use the related parameters (density, mass flow) and use a scaling equation.
freddie_mclair
TL;DR Summary
I have pressure drop measurements at a certain temperature. How can I scale it to other temperatures?
Hi,
I have some measurements for pressure drop of Helium at room temperature and I would like to scale it to other temperatures. Taking into account that, i) the flow is turbulent, ii) the pressure drop, ##\Delta p##, happens always in the same piping and iii) there is only variation on the temperature of the fluid, woud it be sufficient to do:

##\Delta p_T = \Delta p_{RT} \frac{\rho_{RT}}{\rho_T}##

Where ##\rho## is the density and the subscripts RT is for room temperature and T is for other temperature. I can get ##\rho(T)## from thermodynamic tables.
Thanks!

I don't understand what you are trying to do. What would scale and why? Can you post a diagram of the system with states labeled?

Last edited:
There is much more required to determine the pressure drop of a gas in a pipe than you may think. And certainly, the effect of density on pressure drop is not the only factor. The outlet pressure and the viscosity of the gas are also parameters. For how to determine the pressure drop in a pipe for a compressible gas, you first need to know how it is done for an incompressible liquid. For how to do all this, see Chapter 7 of Transport Phenomena by Bird, Stewart, and Lightfoot.

I have measurments of Helium at room temperature across some piping. We have set different mass flows, while always keeping the inlet pressure constant and then we measured the pressure in the outlet. With this we have the pressure drop at different mass flows.
Now, I would like to extrapolate this data to 80K using the pressure drop calculated at room temperature. So, my idea is to do a sort of scaling using the related parameters that change with the temperature, which is the density, and now that I think of it, probably also the mass flow.

## 1. How does temperature affect pressure drop?

Temperature has a direct impact on the viscosity of a fluid, which in turn affects the pressure drop. As temperature increases, the viscosity of a fluid decreases, resulting in a lower pressure drop. This is because the fluid can flow more easily at higher temperatures, reducing the resistance to flow and therefore the pressure drop.

## 2. Can pressure drop be scaled to different temperatures?

Yes, pressure drop can be scaled to different temperatures using the Reynolds number. The Reynolds number takes into account the fluid properties, such as viscosity and density, as well as the flow rate and dimensions of the system. By using the Reynolds number, pressure drop can be accurately scaled to different temperatures.

## 3. Is there a specific equation for scaling pressure drop to other temperatures?

There are various equations that can be used to scale pressure drop to different temperatures, depending on the specific system and conditions. The most commonly used equation is the Darcy-Weisbach equation, which takes into account the fluid properties, flow rate, and dimensions of the system to calculate pressure drop. Other equations, such as the Hazen-Williams equation, may also be used depending on the specific application.

## 4. How does the type of fluid affect the scaling of pressure drop?

The type of fluid can greatly affect the scaling of pressure drop to different temperatures. For example, a highly viscous fluid, such as oil, will have a larger change in pressure drop with temperature compared to a less viscous fluid, such as water. This is because the viscosity of the fluid plays a key role in the pressure drop calculation.

## 5. Are there any limitations to scaling pressure drop to other temperatures?

While pressure drop can be accurately scaled to different temperatures using the appropriate equations, there are some limitations to keep in mind. These include the assumption of laminar flow, which may not be applicable in all systems, as well as the accuracy of the fluid properties used in the calculations. It is important to carefully consider these limitations when scaling pressure drop to other temperatures.

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