Hydraulic Pumps | Fluid Mechanics for Mechanical Engineering PDF Download

Chapter 16

 HYDRAULIC PUMPS

CENTRIFUGAL PUMP

•  Centrifugal pump is reverse of inward flow reaction turbine. It works on princieple of forced vortex  motion. It has high discharging capacity and can be used for lifting highly viscous liquids e.g. sewage water,  chemicals etc.
•   Priming is an operation in which liquid is completely filled in the chamber of pump so that air or gas or  vapour from the portion of pump is driven out & no air pocket is left.
•  In volute pump cross sectional area results in developing a uniform velocity throughout the casing & free  vortex is formed.
•   Centrifugal pump has high output and high efficiency.
•  Head Vs discharge and Power Vs discharge relationship

•   work done persecond = ( )

(If discharge enters without whirl & shock, V_w1 = 0

•   Static head (H_s) = h_s + h_d = static suction lift + static delivery lift
•   Manometric Head (Hm) it is the head against which pump has to do the work.

 - Losses of head in the pump
(or)

where
p_d & p_s are pressures at delivery & suction points.
V_d & V_s are velocities at delivery & suction points.
Z_d & Z_s are position head of delivery & suction points.

•   Efficiencies of the pump

(i) Manometric Efficiency (h_man)

(ii) Volumetric Efficiency (h_vol)

(iii) Mechanical Efficiency (h_mech)

(iv) Overall Efficiency (h_o)
h_o = h_man × h_vol × h_mech

•  The specific speed of a centrifugal pump may be defined as the speed in revolution per minute of a  geometrically similar pump of such a size that under corresponding conditions it would deliver 1 litre of  liquid per second against of a head of 1m.

For multi stage (H_m) =

Specific speed (N_s) =

•   Pumps in Series :

The pumps are connected in series in order to increase the head at constant discharge.
Q₁ = Q₂ = Q₃ = ...
H = H₁ + H₂ + H₃ + ...

•  Pumps in parallel :

The pumps are connected in parallel in order to increase the discharge at constant head.
Q = Q₁ + Q₂ + Q₃ + ...
H = H₁ = H₂ = H₃ = ...

•  Minimum speed needed to start the pumping :

If the pressure head raised is greater or equal to Hm, then pump will start pumping.
Pressure head ³ H_m

Where Hm is manometric head.

•  Speed ratio of pump  

 = 0.95 to1.25

•  Flow ratio of pump

  = 0.1to 0.25

•   For optimum efficiency impeller should be designed such that whirl velocity at inlet is zero. It means  discharge should enter in the pum radially (V_w1 = 0)

Model Laws in Pumps :

D = Outer diameter of impeller
P = Shaft power
H_m = Manometric head
N = Impeller speed in rpm

Characterstic Curve of Pump

•  Cavitation in pumps

The following factors contribute towards onset of cavitation.
(i) High runner speed
(ii) High temperature
(iii) Less available NPSH
For no cavitation, NPSH ³ s_cH
s_c = Critical Thoma’s number = 1.042 × 10^–3 (N_s)^4/3
where Ns is specific speed of pump.
NPSH = (H_a – h_s) – H_v
where, H_a = atmospheric pressure head
H_v = vapour pressure head
h_s = suction head
RECIPROCATING PUMP

Volume of water discharged per second,

A = Area of cylinder (in m²)
L = Length of cylinder (in m)
N = Crank speed (in rpm)

•   If the head against which water is to be lifted is

H_s = (h_s + h_d)
h_s = suction head
h_d = delivery head

•  Work done per second =gQ(h_s + h_d), where g = d_g
•  Reciprocating pumps are used to lift water against high head at low discharge.
•  To increase discharge and to maintain it more uniform, double acting reciprocating pumps are used.

thus power also gets doubled.

•  Slip in Percentage is given by

where C_d = coefficient of discharge
Slip is negative when (i) delivery pipe is small and suction pipe is long (ii) Pump is running at very high
speed.

•  Indicator diagram is a graph between the pressure head in the cylinder and the distance travelled by  the piston flow inner dead centre for one complete revolution of the crank, work done by pump is  proportional to area of indicator diagram.
•  Air Vessel is used to obtain continuous supply of water at uniform rate, to save a considerable amount of work and to run the pump at a high speed without separation.
•  Percentage of work saved is 84.8% when single acting pump with air vessel is used while this saving is only 39.2% when air vessel is used in double acting pump.
•  Advantage of multicylinder pumps are that the pump even without air vessels deliver liquid more uniformly as compared to single cylinder pump.
•  Operating Characteristic Curve of Reciprocating Pump is given below :