Bernoulli's Equation With Losses

[tomtomtom1]

TL;DR Summary

Bernoulli's Equation With Losses

Hello community

I have been trying to get my head around Bernoulli's equation when factoring in energy loss due to friction.

I am trying to understand the concepts and i was hoping someone could remove some doubt from my mind by confirming the following:-

1) Would the following statement be correct:-

Is the above correct?

2) If i wanted to apply this equation to the following open channel system:-

I am certain this is correct could really use someone with some experience to confirm this.

Thank you.

 

[Lnewqban]

That is correct only for a specific rate of flow.
If flow decreases some, losses (due to entrance into pipe, friction, change of direction, entrance into lower tank) decrease at a square rate and $Z_2$ increases accordingly.

 

[tomtomtom1]

That is correct only for a specific rate of flow.
If flow decreases some, losses (due to entrance into pipe, friction, change of direction, entrance into lower tank) decrease at a square rate and $Z_2$ increases accordingly.

Thank you.

 

[tomtomtom1]

That is correct only for a specific rate of flow.
If flow decreases some, losses (due to entrance into pipe, friction, change of direction, entrance into lower tank) decrease at a square rate and $Z_2$ increases accordingly.

Hi Lnewqban

If i can ask a follow on question which is this, if i had the same example but this time i added a pump half way along the pipe then would the gain in energy from the pipe be described in Bernoullis equation as:-

This equation makes sense to me because I interpret this equation as saying that at Point 1 in the system the total energy is the sum of the Pressure + Kinetic + Potential Heads. As the fluid travels to Point 2 it losses some energy due to friction etc and gains some energy due to the pump.

Or would the following be correct:-

I struggle to understand this because at Point 1 there is no gain as the pump is located half way along the pipe but i have been told that this equation is the correct representation of Bernoullis equation when dealing with a pump.

Can you shed any light?

Thank you.

 

[Lnewqban]

If you insert a pump halfway along the pipe, the whole dynamic balance that we had before changes.
A pump would help the flow overcome all the losses previously mentioned, reducing the difference between $Z_1$ and $Z_2$, and even reverting the relative heights of the reservoirs (1 lower than 2), as long as we manage to keep the same rate of flow (which would be difficult to achieve for a centrifugal type of pump, since delivered pressure and flow are inter-dependent for it).
I would select your first equation over the second one.