Assignment on Dimensional Analysis and Hydraulic Machines

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MODULE TITLE : FLUID MECHANICS

TOPIC TITLE : DIMENSIONAL ANALYSIS AND HYDRAULIC MACHINES

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FM - 3 - TMA (v1)

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Published by Teesside University Open Learning (Engineering)

School of Science & Engineering

Teesside University

Tees Valley, UK

TS1 3BA

+44 (0)1642 342740

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of the Copyright owner.

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IMPORTANT

Before you start please read the following instructions carefully.

1. This assignment forms part of the formal assessment for this module. If

you fail to reach the required standard for the assignment then you will be

allowed to resubmit but a resubmission will only be eligible for a Pass

grade, not a Merit or Distinction.

You should therefore not submit the assignment until you are reasonably

sure that you have completed it successfully. Seek your tutor's advice if

unsure.

2. Ensure that you indicate the number of the question you are answering.

3. Make a copy of your answers before submitting the assignment.

4. Complete all details on the front page of this TMA and return it with

the completed assignment including supporting calculations where

appropriate. The preferred submission is via your TUOL(E) Blackboard

account:

https://eat.tees.ac.uk

5. Your tutor’s comments on the assignment will be posted on Blackboard.

Teesside University Open Learning (Engineering)

1. It is found experimentally that the terminal velocity ut of a spherical

particle in a fluid depends upon the diameter d of particle, the

dynamic viscosity µ of fluid and the buoyancy weight W of the particle [given by the difference in density between the particle and the

fluid (∆ρ) × gravitational acceleration (g)]. Determine the nature of the relationship between these variables.

2. (a) Water (density 1000 kg m–3) is maintained at a gauge pressure of

4 MPa in a horizontal pipe of diameter 100 mm. It is passed through

a nozzle of diameter 15 mm which discharges a horizontal jet into the

atmosphere. If the frictional losses reduce the theoretical discharge

velocity by 6% in this process, calculate the actual velocity of the jet

and its flow rate in kg s–1.

(b) This jet strikes an upward curved vane moving at 15 m s–1 in a

horizontal direction away from the jet, which deflects the water

through an angle of 120º. The impact is shockless. Calculate:

(i) the magnitude and direction of the velocity of the fluid leaving

the vane

(ii) the thrust on the vane in a horizontal direction

(iii) the thrust on the vane in a vertical direction

(iv) the power generated by the impact in the horizontal direction.

3. (a) Distinguish, with the aid of simple sketches where appropriate,

between the construction, operation and applications of the Pelton

wheel, Francis turbine and Kaplan turbine.

Teesside University Open Learning (Engineering)

(b) In a Francis turbine, the supply head (H) is 20 m of water (density

1000 kg m–3). The discharge rate to atmosphere is 600 kg s–1. The

external radius of the runner (R1) is 0.43 m and the internal radius

(R2) is 0.20 m. The runner blades are radial at inlet and they rotate at

300 revs min–1. The blades occupy 5% of the circumferential area

and are shaped to ensure that the radial velocity (u1R) is kept constant

and equal to

If the shaft power is 80% of the water power, determine the:

(i) guide vane angle

(ii) blade exit angle

(iii) water power

(iv) diagram power

(v) shaft power

(vi) height of runner blade at inlet and outlet.

4. A centrifugal pump has the following pressure – capacity characteristics:

It is planned to use this for a process having the following system

characteristic:

(a) Determine the operating point for this pump with this system.

Pressure (kPa)

Capacity (m3 h–1)

350

370

400

435

465

100

505

125

545

150

595

175

660

200

725

225

800

250

Pressure (kPa)

Capacity (m3 h–1)

500

495

490

480

465

100

455

125

420

150

395

175

360

200

325

225

285

250

0 2 2. .gH

Teesside University Open Learning (Engineering)

(b) The actual flowrate required by the process is 50 m3 h–1. If the

overall efficiency of the pump at this flowrate is 70%, determine the

power consumed when the liquid being pumped has a density of

1200 kg m–3.

For the same flowrate (50 m3 h–1), this pump has an overall

efficiency of 80%.

(i) Determine the power used by this pump at a flowrate of

50 m3 h–1.

(ii) Would it be a better choice? Give reasons for your answer.

(iii) What other factors should be considered before a final choice is

made?

Pressure (kPa)

Capacity (m3 h–1)

400

395

390

380

370

100

360

125

345

150

320

175

305

200

280

225

255

250

Teesside University Open Learning (Engineering)

5. A process requires the precise control of the flow of a fluid to a reactor

operating at 100 bar pressure (1 bar = 100 kPa). The flowrate may need

to change to match the required reactor output. The flow should be

relatively non-pulsating.

(i) Suggest a suitable pump for this duty. Give reasons for your choice.

(ii) Describe, with the aid of a suitable diagram, the construction and

operation of your chosen pump.

6. It is proposed to pump 1500 m3 of a liquid (density 1100 kg m–3) each

day through a total head of 10 m (including all losses) by using either a

centrifugal pump or a reciprocating pump.

The centrifugal pump discharges 2.0 m3 min–1 when driven by an electric

motor supplying a power of 5 kW.

The reciprocating pump has a discharge rate of 1.75 m3 min–1 when

driven by an electric motor supplying 3.5 kW.

(a) Calculate the efficiency of each pump.

(b) If electricity costs 8p per kWh, select the most economical pump and

determine the cost saving over 300 days of operation.

choice of pump is made.

Teesside University Open Learning (Engineering)

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