UA-24579753-1

FLUID MECHANICS

Water head:

Water head is the distance (in meters) between top water level and a datum line. Fig.1.10 shows water tank with water flow from tank through a vertical pipe. Water head at end of vertical pipe is estimated as the distance between top water level and the horizontal pipe line, i.e. water head = 15 meters. Water head is an indication to water pressure and or water velocity, 10 meters water head equals 1 bar. Accordingly, in the tank shown in Fig.1.10, the pressure gauge reading will be 15/10 = 1.5 bar. Water pressure is not affected by tank volume, as shown in Fig.1.11, two tanks with different volumes and the same height, will give the pressure gauge reading (1.5 bar).

10
Fig.1.10 Water head
11
Fig.1.11 Water head & tank volume

Water flow rate:

Water flow rate in a pipe is measured in number of water volume units (cubic meters = m3) passes through pipe cross section in a time unit (second = s), i.e. water flow rate is measured in (m3/s). Also can be measured in (m3/hr) (Liters/minute = Lit/min) or (Lit/s) or (Gallons per minute = GPM).
If water velocity in a pipe is known, then water flow rate can be determined by multiplying velocity x cross section area. Assuming pipe diameter = d, then
Cross section area = π x d2      in (m2)
                                4
If Water velocity = v in (m/s)
 
So, water flow rate = v x π x d2    in (m3/s)
                                     4
Friction losses:
When water flows inside a pipe, a part of water head is consumed because of frictional losses between water and internal wall of the pipe, which is called “Frictional head loss” or “Pressure loss”. In addition, another part of water head is lost because of water crossing pipe fittings & valves. Total head loss value depends on coefficient of friction of used pipe, number and type of fittings & valves.
In general to estimate frictional head loss in a pipe the following formula can be used:
 
Hf = flv2 / 2gd  
 
Where;
Hf =Frictional head loss in meters (m)
f = Roughness factor
l  = Pipe length in meters (m)
v = Water velocity in (m/s)
g = Gravity acceleration (9.8 m/s2)
d = Pipe diameter
All fittings (e.g. elbows, tee’s, etc) & valves have equivalent lengths in meters that can be added to pipe length in the above mentioned formula to give total frictional head loss.
 

Water pumps:

Water pump is an equipment to increase water pressure. Water pump has several types depending on required function. Domestic water pumps are usually of centrifugal type (Fig.1.12) which will be discussed in this section.Fig.1.13 shows main parts of a centrifugal water pump.
Water pump is defined by its head in meters (or pressure in bars) & discharge or flow rate in m3/hr (or m3/s or Gallons per minute GPM, etc), at certain pump motor speed (e.g. 2900 rpm, rpm = revolution per minute).

pumps

Fig.1.12 Centrifugal pumps – LOWAR ITALY 

13

 

 

 

REF.
No
PART
REF.
No
PART
1
Pump body
9
Tab
2
Suction flange
10
Fill & drain plugs
3
Impeller
11
Fill & drain plug seals
4
Diffuser
12
Mechanical seal
5
Impeller spacer
13
Elastomers
6
Shaft extension
16
Pump body fastening bolts & screws
8
Impeller lock & nut washer
 
 
Fig.1.13 Main parts of centrifugal pump
LOWARA – ITALY

Fig.1.14 shows the relation between pump head (H) & Pump discharge (Q) at constant speed of 2900 rpm. Manufacturers define a working zone for each pump (thick line) which indicates that pump will not give proper performance before and after this zone. Curve shows that as pump discharge increase (more line consumption), as pump head decreases and vise-versa.

14
Fig.1.14 Pump H-Q curve

Pump fluid power (FP);  means the power in KW contained in delivered water from pump;

FP = γQH
Where;
FP = Fluid power in Watts
γ = Water Specific gravity in (N/m3)
Q = Pump discharge in (m3/s)
H = Pump head in (m)
 
Pump brake power (BP);  is required motor power to operate the pump;
BP = FP
         ή
Where
FP = Fluid power
ή   = Pump efficiency
Fig.1.15 Pump ή -Q curve

The difference between FP & BP is lost in mechanical & electrical losses of pump and electric motor. Pump efficiency (i.e. FP/BP) is varied according to pump discharge; Fig.1.15 shows relation between pump discharge (Q) & pump efficiency (ή) at constant speed of 2900 rpm. As shown, maximum efficiency point is called pump Design point, which is the best point (head & discharge) for selecting or operating the pump.

1516

Fig.1.16 Pump P-Q curve

Fig.1.16 shows the relation between required pump power & pump discharge.

Affinity laws; for the same pump with same impeller diameter:

Q α N, i.e. Q1/Q2 = N1/N2
H α N2, i.e. H1/H2 = (N1/N2)2
P α N3, i.e. P1/P2 = (N1/N2)3
Where;
Q = Pump discharge in (m3/s)
H = Pump head in (m)
P = Pump power in (KW)
N = Pump speed in (rpm)
 
From affinity laws, it’s obvious that pump flow rate can be controlled through motor speed control. In fact, controlling of pump flow through speed control is the best method for flow control, where it reduces pump power consumption (P1/P2 = (N1/N2)3 from affinity laws). Controlling of motor speed is obtained through a special device called VFD (Variable Frequency Drive) to change motor frequency according to flow demand and accordingly motor speed.
 
Pump speed; pump speed is affecting pump cost, lower pump speed has higher cost than one of higher speed, i.e. for the same head & discharge a pump with 1450 rpm speed is more expensive than 2900 rpm pump. This results from two major reasons which are; the lower speed pump has longer life time, and the lower noise level of lower speed pump especially for indoor use.
 
Air fans:
Air fans have similar characteristics to centrifugal water pumps. Both are governed by the same laws including affinity laws. Fig.1.17 shows an axial flow fan & Fig.1.18 shows a centrifugal fan. The main difference between axial & centrifugal type fans that centrifugal fan has lower noise level than axial flow fan.
 

axial flow

Fig.1.17 Axial flow fan – VENT – AXIA, UNITED KINGDOM

centrifugalroof 

Fig.1.18 Centrifugal fan – VENT – AXIA, UNITED KINGDOM