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ME2011R

School of Engineering and Applied Science

ME2011 –Thermodynamics & Fluid Mechanics

Deferred/Referred Coursework Summer 2015

You have been deferred or referred in ME2011. To satisfy the deferred or referred requirement you are required to provide full solutions to the following questions. In order that you pass this deferred or referred coursework you must provide FULL and HIGH quality solutions to ALL SIX questions. Untidy working, lack of explanation and misuse of units WILL be heavily penalised. You may use any reference material available to you and have unlimited time to complete the questions. Your solutions must be scanned in and uploaded to the Referred Assessment folder on the ME2011 Blackboard site. The deadline for submission is Wednesday 26th August 2015.

ME 2011R

This examination is subject to the Examination Regulations for Candidates

SECTION 1: Applications of Thermodynamics (answer 2 questions)

1. In an air standard Otto cycle the pressure and temperature of the air at the start of compression is 1 bar and 20°C. The compression is isentropic and the volumetric

compression ratio is 10:1. Heat energy is added at the end of compression at constant

volume until the temperature reaches 2000K. The expansion back to the initial volume

is isentropic and heat rejection is then at constant volume.

a) Sketch the cycle on a p-V diagram: [3]

Determine:

b) The temperature at the end of compression. [5] c) The specific energy added at the end of compression [3] d) The temperature at the end of expansion. [4] e) The thermal efficiency of the cycle. [3] f) The thermal efficiency of a Carnot engine running between the same extreme

temperatures. [3]

g) Briefly explain why the compression ratio in an Otto cycle engine is normally limited to about 12:1. [4]

a) Show that the Carnot coefficient of performance of a reversible refrigerator operating between high (TH) and low (TL) temperature reservoirs is:

[3]

A vapour compression refrigerator, with Refrigerant 134a as the working fluid, has a

refrigerant mass flow rate of 0.004 kg/s and evaporator and condenser saturation

temperatures of -10°C and 40°C respectively. The vapour leaves the evaporator with

10 K of superheat and the liquid leaves the condenser with 5 K of sub-cooling.

Assume the compressor operates with an isentropic efficiency of 0.8 and the

expansion process is isenthalpic.

b) Sketch the process on a property diagram [3] You may use the P-h diagram provided

Determine :

c) The enthalpy of the working fluid at each of the major points in the cycle [7] d) The cooling load of the refrigerator [2] e) The compressor input fluid power required [2] f) The coefficient of performance of the refrigerator [2] g) The Carnot coefficient of performance of a reversible refrigerator operating

between the same evaporator and condenser saturation temperatures. [2]

Briefly comment on;

h) the effect of reducing the condenser pressure to 6 bar [4]

1 ,





H orrefrigeratCarnot

T COP

ME 2011R

This examination is subject to the Examination Regulations for Candidates

3. A vapour power cycle consists of a boiler supplying superheated steam, at 30 bar and 450°C, to a turbine. The steam expands in the turbine to the condenser pressure of

0.2 bar with an isentropic efficiency of 0.75. The turbine exhaust steam is then passed

through the condenser and is sub-cooled to 40°C before being pumped by the feed

pump back into the boiler. The feed pump process can be considered isentropic.

a) Sketch the process on a property diagram [4] and determine: b) The enthalpy and the state of the working fluid at each of the major points in the

cycle [10]

c) The net work output per kg of steam [2] d) The thermal efficiency of the cycle [2] e) The work ratio of the cycle (net work out to total output work ratio) [2] f) Briefly comment on the effect on efficiency of raising the boiler pressure and what

limits the pressure to which it can be raised? [5]

ME 2011R

This examination is subject to the Examination Regulations for Candidates

SECTION 2: Fluid Mechanics (answer 2 questions)

4. Two pipes in series (A & B) connect two reservoirs, as shown in figure Q4. Pipe A is 155m long, falls 15m in height and has a diameter of 75mm. Pipe B is 120m long, is

horizontal and has a diameter of 150mm. There is a sudden expansion piece from

75mm to 150mm diameter between the two pipes. The water level in the high

reservoir is 3m above the pipe entrance and the level in the low reservoir is 2 m above

the pipe exit. There are open valves in place at the pipe A entrance and the pipe B exit

Assume:

 Friction factor (all pipes), f = 0.006

 Entry loss = 0.5 (u²/2g)

 Exit loss = 1 (u²/2g)

 Sudden expansion loss = (1-(DA 2/DB

2))2(uA²/2g) - based on flow though A

 Valve loss (open) = 0.2 (u²/2g)

Calculate:

a) The velocity of water in both the A and B pipes [12] b) The total volume flow rate in cubic metres per hour between the reservoirs [3]

c) A single pipe, C, is laid in parallel to pipes A & B to increase the total volume flow rate by 50%. Estimate the required minimum diameter for the pipe C, stating

what assumptions you have made? [10]

2 m

15 m

3 m

155 m

120 m

Figure Q4

ME 2011R

This examination is subject to the Examination Regulations for Candidates

5. The following results were obtained from a test on a single stage centrifugal pump running at constant speed of 1480 rev/min with a working fluid of water:-

Delivery: Q m³h-1 26.5 20.6 13.9 9.1 3.4 0

Total head H m 9.3 12.6 15.4 16.9 17.8 18.4

Overall efficiency:  % 58.9 63.3 58.9 47.5 22.4 0

Two similar pumps are connected in parallel with common suction and delivery pipes

of 75 mm diameter. The system static lift is 6 m and the pipework length is 85 m.

Take the coefficient of friction, f, to be 0.006.

a) Calculate and tabulate the flow rates, pump heads and efficiencies for the two pumps in parallel using the single pump data shown. [3]

b) Calculate and tabulate the system head for the actual system.[8] c) Use the provided graph in Appendix Q5 to plot the ‘2 pump’ and the system head

characteristics and estimate the ‘2 pump’ delivery, head and pump efficiency [4]

d) Calculate the total shaft power required to drive the pumps. [3] e) If one pump is removed from the installation what will be the delivery obtained

from the one remaining pump and what will be its power consumption? [3]

f) Briefly comment on the advantages of using 2 pumps in parallel instead of a single pump. [4]

ME 2011R

This examination is subject to the Examination Regulations for Candidates

6. A hydraulic turbine is required to be designed to produce 5 MW under a head of 50 m of water at a speed of 200 rev/min. A geometrically similar model with an output of

12 kW and a head of 10 m is to be tested in water under dynamically similar conditions.

Neglecting Reynolds number differences between the prototype and the model

determine:

a) The speed at which the model must be run [10] b) The required impeller diameter ratio between the model and the prototype [5]

The model is tested and a flow rate of 150 litres per second is found to give the

required power output. Determine:

c) The efficiency of the model. [5] d) The volume flow rate required through the prototype turbine [5]

It can be shown for a hydraulic turbo machine that:

 

-3 -1

-1 -1 3 -1

power W density kg m speed rad s

diameter m fluid viscosity kg m s flowrate m s

head m gra

W N

D Q

H g





        

  -2

vitational constant m s   

223

tcoefficien Head,tcoefficien Flow

number Rey noldsRe,tcoefficienPower

Where

))((Re)(

W P















ME2011R

APPENDIX Q5

0 10 20 30 40 50 60

E ff

ic ie

n c y

(% )

H e a d

( m

)

Flow Rate (m³/h)

Pump Characteristics