# Question about Fluid Mechanics, pumping

1. Apr 29, 2015

### Junkwisch

1. The problem statement, all variables and given/known data
The water in the bottom tank (position 1) is pumped into!the!roof tank (position 2) through a long pipe (containing two elbows a and b separated by 1 meter) which discharges freely at a height 50 cm above the liquid surface in the upper tank. To fill up the upper water tank when it’s needed, the volumetric flow rate used is!800 litres per minute which ensures that the height difference between the liquid surfaces in the tanks is maintained, even over the peak demand period. All piping between point 1 and 2 have an internal diameter of 65mm with an absolute roughness of 0.005mm. Ignore pipe entry and exit losses. Between point 2 and 3 and between point 2 and 4 all pipes have a diameter of 40mm with an absolute roughnessof 0.004mm.

$Q=800\frac{Litres}{minute}$
Building height is 200m
Both point 1 and 2 are at free surface of water

Patm=101.3kPa
Pvap=3.169kPa
Pressure above free surface = Patm+100kPa
$ρ=1000\frac{kg}{m^3}$
μ=0.001Pa.s
Mechanical efficiency = 0.62
NPSHR=2m

*Leq for elbows were not given "I assume 0"
"See attachment for drawing"

Question 1
Calculate the power that the bottom pump (Pump1_2) needs to provide to the liquid to supply the roof tank at a flow rate of 800 litres per minute/

Question 4
To get the required tap pressure (3 bars gauge) at floor 10 (considering that floor 0 is on the ground), calculate the Leq of the pressure reduction valves at this floor, in order to get 3 bars of gauge pressure after the valve. The volumetric flow rate required through the tap is 3.33.10[3 m3 /s. We assume that a valve is situated 1 meter horizontally after an elbow c.

Only the losses between point 2 and a point just after the valve servicing floor 10 need to be included in the calculations for part 4.

Question 5
To supply the same tap pressure (3 bar gauge) to the top floors of the building a pump is required on the roof as well, as the static pressure is not high enough. How many floors need to be supplied through the roof pump to ensure a gauge pressure of 3 bars at the tap?
2. Relevant equations
Mechanical energy balance equation: $\frac{ΔP}{ρ}+\frac{ΔV^2}{2*α}+gΔz+Ws+F$ (Ws is the work done by pump)

Continuity equation: $Q1=Q2$ (I couldn't get subscript to work)
Pressure equation: $P2=P1+ρ*g*h$
Volumetric flow rate: $Q=V*A$
Reynolds Number: $Re=\frac{ρ*V*D}{μ}$,
Relative roughness: $\frac{e}{D}$
Fanning friction factor, ƒ depends on Re and relative roughness "value taken from Moody's chart"
$F=\frac{2*ƒ*V^2*L}{D}+0.5*K*V^2$
3. The attempt at a solution
for all pipe with diameter of 65mm, $Re=261,178$ relative roughness=0.0000769 Fanning friction factor=0.0038

for all pipe with diameter of 40mm, $Re=106,000$ relative roughness=0.0001 Fanning friction factor=0.0045

For Question 1
I used mechanical energy equation to find the work done by the pump. I assume that P1, is the pressure at the entrance of the pump (from point 1). It can be calculated by Pressure equation: $P1=Patm+ρ*g*h$. The problem for this question is P2, since the water in the pipe freefall 50cm before reaching point 2 (or the water level in tank2), is it okay for me to use the Pressure above free surface = Patm+100kPa as P2? or P2 should be equal to the atmospheric pressure?

For Question 2 and 3, I don't have any problem here (assuming my Q1 is correct).

Question 4
I tried using the same equation as of question 1 to calculate the pressure before it reached the valve.
$P1=Patm+ρ*g*h$., due to h being around 167m, P1 is in million of Pascal. By using mechanical energy balance equation with. ΔV,Δz and Ws equal to 0. I can calculate Leq but the answer I got is larger than the height of the building itself.

What is the correct way of calculating pressure at point before entering the valve?
(I also tried the mechanical energy equation for the pressure after it fall from point 2 to the elbow of floor 10, the pressure got smaller, but Leq is still over 300 metres).

Question 5
I haven't start this since I'm uncertain about how to calculate pressure similarly to question 4

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• ###### 11198558_725492797568501_1180931178_n.jpg
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2. Apr 29, 2015

### paisiello2

1) Where does the 100kPa come from?
4) Maybe show your work explicitly here to see where you went wrong.

3. Apr 29, 2015

### Junkwisch

Hi, for question 1
I assume you mean the pressure above the free surface of tank 2 which is, P2=Patm +100Kpa?
If it is, this value is given by the question

This is my working out for question 4, showing the two formulas I used

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4. May 9, 2015

### Miapana

I am having difficulty with question 4 of this assignment ... Do we or do we not condSider any valves at the elbows ?
If somebody would please clarify it would be greatly appreciated

5. May 9, 2015

### Junkwisch

Only for floor 10, the pressure reduction valve, 1metre after the elbow

6. May 10, 2015

### Miapana

Sorry I actually meant qn 5, this is why I shouldn't leave assignments to the last minute !

7. May 10, 2015

### Junkwisch

I don't think you have to, we only need to calculate the pressure before it enter the valve