Question

in fluid mechanics, does the gage pressure influence the velocity?

Answer 1

of the fluid flow?

Answer 2

Perhaps, but we need to look closer into the causation.

Let's take a simple example of fluid flow where Bernoulli's Principles holds and there is no change in potential energy. \[{v^2 \over 2} + {p \over \rho} + gz = constant\]

If the flow passes through a converging nozzle (one that reduces in diameter along the flow direction), we will observe that velocity increases. Take a garden hose for example, place your thumb over the opening, which reduces the diameter, and you'll see an increase in velocity. If we hook up a pressure gage to the hose, we will see that the gage pressure decreases as the velocity increases because\[v ~ \alpha ~ {1 \over p}\]
This can be observed in the attacked image titled "VenturiFlow"

By the same token, if we increase pressure, we will decrease velocity.

This, of course, relates purely to "passive" devices. That is to say, devices that do not add or remove energy from a system.

I can present a thermodynamic approach if you wish to study "active" devices, such as pumps and turbines, which do add or remove energy from the system.

Answer 3

thank you taking the time to answer this question. in that sense i can see that pressure is inversely proportional to velocity at an outlet ( the end of the water hose) but what aboout at the inlet?

in my case I have one inlet and two outlets, one of the outlet velocities is unknown...i am not sure if i should use bernoulli's equation or Q=V1*A1=V2*A2+V3*A3 to find the unknown velocity.

Answer 4

the inlet gage pressure is 10 psi

Answer 5

since both the velocity and gage pressure are in the same direction

Answer 6

That equation is definitely the better approach for this problem if and only if certain criterion are met. Let's rewrite the volumetric flow rate equation you have given such that it becomes a conservation of mass equation. \[\dot m ={ \rho_i V_i A_i} = \rho_2 V_2 A_2 + \rho_3 V_3 A_3\]

The criterion I spoke of relate to the relative densities at the inlet and exit. Obviously, the conservation of mass equation I presented is robust, but it may be hard to fix the densities. If the flow is incompressible, Mach numbers much less than 1, than we are okay to use the volumetric flow rate equation. If the fluid, in and of itself, is incompressible, than we are okay to use the volumetric flow rate equation. These are closely related, but both are worth mentioning.

Now, back to your question. If the flow is indeed incompressible, and the areas are all known, its simple plug-and-chug. Indeed, you will see a change in pressure from the inlet to the two exits.

Answer 7

thanks again Mr. Eashmore!