Slides 5 Hydraulic Machinery

7/29/2019 Slides 5 Hydraulic Machinery

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PUMPS

CHAPTER 5

HYDRAULIC MACHINERY


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Types of hydraulic machines

Two categories:

Pumps

Machines which give energy to fluid are called pumps

2. TurbineMachines which take energy from fluid are called turbines

Pumps and turbines can be divided into :

Positive displacement units (piston & diaphragm pump)

Continuous flow units/rotodynamic (turbines)

Radial flow machines (centrifugal pumps), axial flow machines

and mixed flow machine


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Pumps function

Used to transfer fluid in system, either at the same level or to a

new height.

The flow rate depends on the height to which the fluid is pumped.

The relationship between head and flowrate is called pumpcharacteristic


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Selecting a pump

The nature of liquid to be pumped

The required capacity (volume flow rate)

The conditions on the suction & discharge (inlet & outlet) side of

pumpThe total head on the pump

The type of system to which the pump is delivering the fluid

The type of power source (electric motor, diesel engine, steam

turbine etc)Space, weight and position limitation

Environment condition

Cost : pump purchasee, installation andoperation


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Dimensionless parameters for hydraulic machines

For hydraulic machines, the quantities usually considered in a

dimensionless analysis are:

Quantities Dimensionlessformula

Drotor diameter [L]Qdischarge through pipe [L3T-1]Nrotational speed [T-1]Henergy [L]ggravity [LT-2]

- density [ML-3]- fluid density [ML-1T-1]

P power transferred between

fluid and rotor[ML2T-3]


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The dimensionless coefficient

Modern hydraulics turbines and centrifugal pumps are highly

efficient machines with few differences in their characteristics.

For each design there is a definite relationship between;

The speed of rotation, NDischarge of flow ,Q

Head, H

Diameter, D of the rotating element

Power, P

Power, discharge and head coefficient are given as


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And for homologous machines, the following equations relate the

size, head, flow rate, speed and power between models and

prototype.

, ,

And the specific speed represented by

For turbine, the specific speed and the turbine efficiency arerespectively given as

and


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Example 1

A centrifugal pump discharged 0.017 m3/s against a head of

16 m when the speed was 1200 rpm. The diameter of the

impeller was 300 mm and brake power was 4.0 kW. A

geometrically similar pump 350 mm in diameter is to run at 1700

rpm. Assuming equal efficiencies,

what head will be developed

how much water will be pumped

what brake power will be developed


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Example 2

In order to predict the behavior of a small oil pump as a

prototype, tests are to be made on a model using air. The oil

pump is to be driven by a 30 W motor at 1500 rpm and a 186-

W motor is available to drive the air pump at 450 rpm. Using oil

of specific gravity 0.912 and air of constant density at1.23kg/m3, find the size of model that should be built?


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PUMP TYPES

POSITIVE DISPLACEMENT

Reciprocating

piston

DiaphgramCONTINUOUS FLOW/ROTODYNAMIC

Radial flow machine (eg centrifugal pump)

Axial flow machine

Mixed flow machine


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Pump system analysis

considered pumps that are integrated into a pipe system

Simple pump-pipeline system

Multiple pump system

a) Parallel Operation/Pump in Parallelb) Series Operation/Pump in series


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Simple pump-pipeline system

A pipe delivers a liquid from a lower tank to a higher tank through astatic lift HST at a discharge Q.

The total head generated by a pump is also called the manometrichead (H) since it is the difference in pressure head recorded bypressure gauges connected to the delivery and inlet pipes on either

side of the pump when the pipes are of the same diameter.The pump must generate a total head equal to HST plus the pipelinehead losses.

The following variables are defined:

hld = head loss in delivery pipe (friction, valves, etc)

hls = head loss in suction pipe (entry, bend, etc)Applying the Bernoulli equation to section (1) to section (2) gives,

Since HST=Z2-Z1, the equation can be rearranged as


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Example for simple pump-pipeline system

Calculate the steady discharge of water between the tanks and the power

consumption in the system as shown in figure below. Pipe diameter

(Ds=Dd)=200 mm. The delivery pipe is 2000m long; surface roughness size ks

= 0.03 mm. Losses in valves, bends plus the velocity head amount to

6.2V2/2g. Static lift = 10.0 m.

Q (l/s) 0 10 20 30 40 50H (m) 25 23.2 20.8 16.5 12.4 7.3

(%) - 45 65 71 65 45


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Solution :

Solve simultaneously the head-discharge relationship for pump and system

For the system, use the system equation to determine the head

The ks/D = (0.03/200)=0.00015, obtained from Moody diagram

and

Plot the H and against Q (a graphical solution to interpret the matching ofpump and the system)

Q 10 20 30 40 50Re (x 105) 0.56 1.13 1.10 2.25 2.81

0.021 0.0185 0.0172 0.0165 0.0160hf (m) 1.08 3.82 7.99 13.63 20.65hL (m) 0.03 0.13 0.29 0.51 0.80H (m) 11.11 13.95 18.28 24.14 31.45


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Take discrete values of hf and calculate V and Q from Darcy and

Colebrooke-White equation,

hf (m) 2 4 6 8V (m/s) 0.45 0.66 0.97 1.4Q (l/s) 124.06 20.57 30 43.61hL (m) 0.06 0.13 0.29 0.61H=Hst + Hlosses (m) 12.06 14.43 18.29 26.61


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Multiple pump system : Pump in Parallel

contains several pumps in a parallel arrangement

This is the common feature of sewage pumping stations

head (H) across all the pump will be same no matter how many pumps are

operating.

Whatever the H may be, each pump will be discharging a rate of flowconsistent with the H-Q curve for that particular pump

the total discharge from all the pumps will be the sum of those discharges.

If the pumps have identical performance characteristics, the total discharge

would simply be nQ, where n is the number of pumps in operation.


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Multiple pump system : Pump in Series

less common than parallel pump installation

For series installation, the discharge will be the same through each pump

the total head for the combined operation will be the summation of H for

each pump having the given Q.

It should be noted that all pumps in a series system must be operatingsimultaneously.


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Pump efficiency

Pump efficiency is calculated from, =Q p/W

Where

Q : flow through each pump and p is the pressure across it.

In series, the flow through each pump is equal to the measured

flow, but pressure rise across the upstream pump is

approximately (p1-p2)

For parallel flow, the flowrate through each pump is half the

measured value.

Slides 5 Hydraulic Machinery

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