# A Question on Fluid Pressure

## Main Question or Discussion Point

Hey Everybody! It's my first time posting here, so please forgive any

errors that might creep into this post.

I'm a guy who loves physics. In fact, it has been my favorite subject ever

since I can remember, and in physics, the field that attracts me the most

is kinematics. Well, the question I have is about fluid flow, specifically,

the pressure of a fluid. I've never been good at fluid dynamics and

kinematics so if this sounds like an idiotic question, I'm sorry in

Everywhere I read, it is said that fluid pressure is inversely related to

the speed of the flow. Meaning that if a fluid is flowing through a pipe at

a flow rate of say, 10Kg/second, it will be exerting more pressure than it

would if it were flowing at a rate of 5Kg/second. Basically, it means that

in order to increase the pressure of a fluid, you have to slow it down and

expand its volume. This seems so counter-intuitive! By extension, if a

fluid is at rest, mass flow rate is 0Kg/sec and it's volume is made

infinite, it must have infinite pressure?! This means that the air in the

room I'm sitting should be at an infinite pressure and crush me

immediately! But that is not the case.

Basically, what I'm saying is that if I can increase the pressure by

decreasing the speed of fluid flow, then is not a fluid at rest also at

infinite pressure?

So what is pressure? I always thought that pressure was generated by

confining a large amount of fluid in a small volume. The more the fluid and

the smaller the volume, the higher the pressure. Am I right or wrong? And

what's with the fluid pressure while it's flowing?

I look forward to your answers as I have registered with physics forums

Thanks,
Mak.

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mfb
Mentor
Everywhere I read, it is said that fluid pressure is inversely related to
the speed of the flow.
Higher pressure corresponds to a lower velocity (in equilibrium), but this does not imply a constant pressure/velocity ratio.
Instead, $\frac{v^2}{2}+\frac{p}{\rho}$ is constant, where v is the velocity, p is pressure and rho is the density of the fluid. With zero velocity, you get a maximum, but finite pressure.

Volume is completely unrelated here - and in most cases, it is a good approximation to assume that liquids[STRIKE]fluids[/STRIKE] cannot be compressed at all. Air is a gas, not a liquid[STRIKE]fluid[/STRIKE].

The more the fluid and
the smaller the volume, the higher the pressure.
Assuming a constant temperature: Right.

Edit: Sorry, was confused.

Last edited:
Volume is completely unrelated here - and in most cases, it is a good approximation to assume that fluids cannot be compressed at all. Air is a gas, not a fluid.
This is completely wrong. All gases are fluids by definition. Conversely,
all liquids are fluids, but not all fluids are liquid.

Thanks for the replies guys! but I still have doubts regarding this. Which direction is this pressure being exerted? I'll simplify my question,

If I were to give you two pipelines carrying the same fluid, with the following constraints:

1. Both pipelines carry the same amount of fluid in Kg/s
2. Fluid in both pipelines is at the same temperature
3. Same fluid in both pipelines, so no diff. in viscosity, density or other flow characteristics and physical properties.
4. Both pipelines are parallel to the ground with no slopes of any kind
5. Flow is streamlined in both pipelines, no turbulence of any kind

AND

6. One pipeline has a cross sectional are of 100 cm^2 and another has a cross sectional area of 1000 cm^2

In which pipeline is the fluid at a higher pressure?

OR

Which pipeline has the higher pressure?

Can you answer the question once considering the fluid to be a liquid (more or less incompressible) and once considering it to be a gas?

Hi TheMak,

Both the fluids are flowing at the same mass flow rate. As fluid properties are also the same, the volumetric flow rate may also be considered to be equal.

As the pipes have different cross sectional areas, the fluid velocities would be different. Pipe A with the smaller cross sectional area of 100 cm^2, will have a higher velocity compared to pipe B with the larger x-sectional area of 1000 cm^2.

Pipe A will have a higher pressure compared to pipe B.

The results would not change if considering a gas or a liquid.