# Hydraulic head as a function of flow rate

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1. Oct 27, 2018

### Ronanvdv

Hello!
1. The problem statement, all variables and given/known data
Symbols and variables:

$\dot{V}$ : flow rate
$H$ : Hydraulic head
$g = 9.81 \frac{N}{kg}$
$P_{atmosphere} = 101325Pa$
$\rho = 1000\frac{kg}{m^3}$
I am given a piping system, with serie and parallel pipes, they start from one point and go back in to one point.

I need to plot the hydraulic head (the medium in the piping system is water at 20°C, and the local flow loses are negligible) in function of the flow rate, for $H(\dot{V}=0 \frac{m^3}{s})$ to $H(QMax)$.
With $QMax$ the flow rate where the hydraulic head is 3 times the hydraulic head by zero flow.

The question:
1. How can I calculate the hydraulic head by zero flow
2. How can I calculate the maximal flow rate
My instruction paper is in dutch (reason why i didn't upload it)
2. Relevant equations
In my instruction paper:
$$H = \frac{P_{In} - P_{atmosphere}}{g\rho}$$
Further the mechanical equation out of my syllabi:
$$H_1 - H_2 = R\dot{V}$$
3. The attempt at a solution
In appendix.
I also includes a plot from what I think the solution is. (hydraulic head in function of flow rate)

But what i don't understand, how can (according to my solution) the hydraulic head be negative.
Does someone know how or knows a resource.

Good day!

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2. Oct 31, 2018

### Staff: Mentor

Is there a diagram?