I About Bernoulli's equation for fluid flow

[samy4408]

Hello, I am currently studiying Bernoulli's equation and I have trubble understanding something , say we have a horizontal hose (no change in altitude of pressure ) Bernoulli's equation state that an ideal fluid can flow thought the hose with the same velocity , does an ideal fluid need a pressure gradient to flow thought this hose ?

 

[Lnewqban]

Yes.

 

[samy4408]

Yes.

it does ? so we have a change in pressure between two points in the hose, so the velocity is not constant ?

 

[russ_watters]

it does ? so we have a change in pressure between two points in the hose, so the velocity is not constant ?

No. Continuity demands that velocity be constant because there's nowhere else for the water to go.

Note, with the standard/ideal Bernoulli equation there is no loss, but in the real world there is (due to friction).

 

[samy4408]

No. Continuity demands that velocity be constant because there's nowhere else for the water to go.

Note, with the standard/ideal Bernoulli equation there is no loss, but in the real world there is (due to friction).

that makes sense thanks a lot!

 

[Lnewqban]

That energy consumed by friction comes from the internal energy of the fluid in the way of static pressure, since the flow remains constant and height does not change.
If you could measure velocity and static pressure between two distant points, you would see that the value of velocity remains the same, but the value of static pressure downstream is lower than the one upstream.

Please, see:
https://www.tec-science.com/mechanics/gases-and-liquids/pressure-loss-in-pipe-systems/

That is the reason for the need of a circulating pump in a closed loop of constant height: you need to increase the pressure of the fluid between the end and the beginning of the loop by transferring mechanical energy from the pump into the fluid.

 

[boneh3ad]

That energy consumed by friction comes from the internal energy of the fluid in the way of static pressure, since the flow remains constant and height does not change.
If you could measure velocity and static pressure between two distant points, you would see that the value of velocity remains the same, but the value of static pressure downstream is lower than the one upstream.

Please, see:
https://www.tec-science.com/mechanics/gases-and-liquids/pressure-loss-in-pipe-systems/

That is the reason for the need of a circulating pump in a closed loop of constant height: you need to increase the pressure of the fluid between the end and the beginning of the loop by transferring mechanical energy from the pump into the fluid.

That's only true in a viscous flow. Bernoulli's equation does not apply in that situation without modification for viscous losses.

In a truly ideal flow, you do not need a pressure gradient to sustain a flow. Applying a pressure gradient to an ideal flow results in acceleration.

In a real (viscous) flow, you need a pressure gradient that exactly balances the viscous shear stress to maintain a constant flow rate.