Pump height / NPSH / Bernouilli Equation - Exam Q

Mar 2020
2
0
Ireland
Question:
A centrifugal pump has an NPSH of 4 metres. It is used to transfer hot wort from kettle, open to atm prsssure, to a whirlpool. Calculate the minimum vertical distance the pump must be positioned below the outlet of the kettle to enable effecient pump operation.

Wort flow rate is 200 hl h-1
Vapour pressure of wort at 100 degrees C = 99 kPa
Wort density = 1065 kg m-3
Pipe length from kettle to pump inlet = 8.5 m
Pipe internal diameter = 75 mm
Pipe friction factor = 0.002
Acc due to grav = 9.81 m s-2
Atm pressure = 101.3 kPa

They've given NPSH = (Ps - Pvp)/qg
Where Ps = Suction pressure at pump inlet
Pvp = vapour pressure of liquid at temp of pumping
q = density of liquid
g = acc due to grav

They've also provided Darcys friction Equation

The examiners tip (its a past exam paper) said that people used equations that enable fast solutions, but expected way was Bernouilli Eq.

Bernouilli Eq:

P2/q + (V2^2)/2 + gz2 = P1/q + (V1^2)/2 + gz1

So P2 is 99,000 Pa
q = 1065 kg m-3
V2 is 200 hl h-1
Z2 = 8.5m

P1 = atmospheric pressure?
I dont have V2
Im looking for z1.

Please help me solve this, answer should be 3.94 m
 
Mar 2020
2
0
Ireland
So ive made some progress:
I need to get the velocity:

200hl / h-1
= 3.33 hl/min
= 333 L/min
1L/min = 10^-2 m^3/min
333L/min = 0.333 m^3/min
= 0.00555m^3/sec

Cross Sec Area
= 3.14(0.075/2)^2
= 0.0044

Velocity = Flow/Cross Sec Area
= 1.26 m/s

I followed Darcys Eq on this link:

Δpmajor_loss = λ (l / dh) (ρf v2 / 2)
(0.002) (8.5m)/(0.075m) (1065kgm-3)(1.26)^2 /2
=191.56
Can you give me the correct answer here if this is incorrect

The minimum vertical distance is shown in this formula: Book link

Hmax = (Pl - Pv)/qg - NPSH + V(1^2-Vs^2)/2g - Friction

Hmax =
(101300Pa - 99,000Pa)/(1065kgm-3)(9.81m/s) - 4m + (1.26^2)/(2)(9.81m/s) - 191.45
= 0.2201 - 4m + 0.0809 - 191.56
= -3.699 - 191.56

I think im nearly there with that Hmax formula if I could get the friction by Darcys Eq right. Can you finish this off for me so I can see how to get the 3.94 metres please.