# For a fluid travelling in a tube, if the pressure is decreased at a constant temperature, how does it affect the velocity and fluid density?

I am interested in understanding the relationship between pressure and velocity, as well as pressure and fluid density.

I know that the principle of Bernoulli states that there exists a relationship between the terms. But I'm confused as to wether reducing the pressure of a fluid flowing in a closed tube, would increase the velocity at which the fluid is travelling.

Does this relate to the Drag Force Equation?

• Apparently you are assuming that the fluid is compressible. Is the tube of constant cross sectional area? Is the flow steady (not changing with time)? – Chet Miller Aug 7 '18 at 11:55
• Normally, one worries about the pressure drop through a pipe or tube. You want to decrease the pressure of the fluid in your tube. What do you want to do with the pressure drop ($\Delta P$) in your tube? – David White Aug 7 '18 at 15:15
• Hi @ChesterMiller, thanks for responding. In the question above I was assuming that the fluid is ideal (non-compressible), the cross sectional area and the flow rate are constant. – Aidan Aug 8 '18 at 13:14
• Hi @DavidWhite, thanks for posting a comment. I want to know if by dropping the pressure the fluid will flow faster through the tube. – Aidan Aug 8 '18 at 13:20
• @AidanDeaves, there are standard methods for calculating flow. Flow rate depends on the pressure difference across the tube. For liquid flows, which are incompressible, I would expect the flow rate to remain constant for a constant pressure drop, even as the total pressure was decreasing. For a gas or vapor flow, the fluid density goes down as the pressure goes down. This means that pressure drop increases for a given mass flow rate. I suspect that the pressure drop would decrease slightly for a constant volumetric flow rate, but I would have to run a calculation to verify this. – David White Aug 8 '18 at 17:30

## 1 Answer

For an ideal incompressible inviscid fluid, the Bernoulli equation tells us that the pressure drop in a tube of constant diameter is zero, irrespective of the fluid velocity. Changing the absolute level of the pressure has no effect on this.

For a real (viscous) fluid, the pressure at the inlet to the tube must be higher than the pressure at the outlet, in order to overcome viscous friction. There is a direct relationship between the volumetric throughput rate of the fluid (and the fluid velocity) and the pressure drop along the tube. The higher the pressure drop, the higher the volumetric flow rate. If the fluid is essentially incompressible, changing the absolute levels of the pressures at the inlet and outlet by the same amount has no effect. The pressure drop-flow rate behavior of real viscous fluids can be predicted using the Darcy-Weisbach correlation.