School of Engineering and Design SED06: Examinations Cover Sheet
SUBJECT AREA: MECHANICAL ENGINEERING

Module Code: Module Title:

ME1301 THERMOFLUIDS

Date-Month:

MAY

Year: 2011

Time allowed Hours:

THREE

Answer FOUR questions: TWO from Section A, TWO from Section B.

Examiner(s): Dr T Megaritis and Dr R Kirby Special Stationery Requirements:

Thermodynamic and Transport Properties of Fluids, GFC Rogers and YR Mayhew.

Only School approved calculators are allowed. Use a separate answer book for each section. If you submit answers to more questions than specified, final marks for the examination will be determined using the best marks which satisfy the rubric.

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SECTION A A1. (a) Define what is meant by a streamline, a pathline, a streakline and a streamtube. When are the streamlines, pathlines and streaklines identical? [25%] Write down Bernoulli’s equation and define all the terms that appear in the equation. [20%] Water flows vertically upwards through a pipe which tapers from a cross-sectional area of 0.3 m2 at section A to 0.15 m2 at section B. Section B is located 6 m above section A. At A the flow velocity is 1.8 m/s and the static pressure is 117 kN/m2. Neglecting all losses, determine: (i) (ii) (iii) The water volumetric and mass flow rates. The velocity of water at section B. The water static pressure at section B. [15%] [15%] [25%]

(b)

(c)

DATA Gravitational acceleration g = 9.81 m/s2 Density of water = 1,000 kg/m3

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A2. (a) Write the Continuity Equation for a steady, one-dimensional flow and define each term in the equation. If the flow is incompressible what is the simplified form of the equation? [20%] Explain what are the velocity, contraction and discharge coefficients of an orifice. Write the equation that relates the three coefficients. [20%] A sharp edged orifice has a diameter of 50 mm and is used to measure the flow rate of a liquid discharged from the side wall of a reservoir to the atmosphere. The orifice is located at a depth in the reservoir where the gauge pressure is measured to be 1 bar. The relative density (specific gravity) of the discharged liquid is 0.85. Considering the liquid flow out of the reservoir through the orifice as horizontal and incompressible, determine the theoretical volumetric flow rate of the liquid through the orifice (i.e. the flow rate determined assuming that losses are negligible). [30%] The measured (actual) flow rate of the discharged liquid through the orifice studied in part (b) is 18 l/s. If the diameter of the formed vena contracta is 39.5 mm, determine: (i) (ii) (iii) The discharge coefficient of the orifice. The contraction coefficient of the orifice. The velocity coefficient of the orifice. [10%] [10%] [10%]

(b)

(c)

(d)

DATA Gravitational acceleration g = 9.81 m/s2 Density of water = 1,000 kg/m3

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A3. (a) Describe briefly the main causes of head loss in a fluid flow system. [15%] A liquid fuel is pumped at a rate of 1 m3/s through a 1,000 m long pipe. The internal diameter of the pipe is 500 mm and its inner wall roughness (absolute) is 0.05 mm. The friction coefficient f of the pipe is given by:

(b)

f  0.07    d

  3

1

where  is the roughness (absolute) of the inner wall of the pipe, and d is the internal diameter of the pipe (i.e. (i)

 is the relative roughness). d

Determine the Reynolds number of the liquid fuel flow. Is the flow laminar or turbulent and why? [25%]

(ii)

Calculate the head loss due to friction for the pipe. [20%]

(c)

To reduce the pumping costs, a new pipe of different diameter is to be used. The roughness  of the new pipe is the same as that of the original pipe. The friction coefficient of the new pipe can also be determined using the formula provided in part (b). (i) Let dn be the internal diameter of the new pipe, dor the internal diameter of the original pipe, and a the ratio of the head losses due to friction of the two pipes given by:

a

hL,f ,n hL,f ,or

where hL,f,n is the head loss due to friction for the new pipe and hL,f,or is the head loss due to friction for the original pipe. Derive an equation that gives dn as a function of dor and a. [35%] (ii) Determine the internal diameter of the new pipe for which the head loss due to friction will be half of the head loss of the original pipe of 500 mm diameter. [5%]

DATA Gravitational acceleration g = 9.81 m/s2 Kinematic viscosity of liquid fuel = 0.6 mm2/s

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A4. (a) Explain the physical mechanisms that result in the difference in the relationship between the friction coefficient and the Reynolds number and relative roughness of a pipe, in the cases represented by the ‘smooth pipe’ line and the ‘rough pipe’ region that are indicated in the Moody diagram, shown on page 5. [20%] An oil of 0.85 relative density (specific gravity) is pumped to a reservoir at a flow rate of 10,000 kg/min. The pipe is 1,800 m long and has an inner diameter of 400 mm. Determine: (i) The volumetric flow rate and the velocity of the oil in the pipe. [20%] The frictional head loss in the pipe if the friction coefficient is 0.0075. [20%] The exit head loss at the pipe/reservoir junction. Note that in general the head loss hL due to a sudden enlargement of the cross sectional area of a pipe is given by:
 V2  A V2  A hL  2  2  1  1 1  1  2 g  A1 2g  A2  
2 2

(b)

(ii)

(iii)

where A1 is the cross sectional area upstream of the enlargement, A2 is the cross sectional area downstream of the enlargement, V1 is the fluid velocity upstream of the enlargement, and V2 is the fluid velocity downstream of the enlargement. [20%] (iv) The power required by the pump to overcome the frictional and the exit losses. Assume that the pump has an efficiency of 100%. [20%]

DATA Gravitational acceleration g = 9.81 m/s2 Density of water = 1,000 kg/m3

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SECTION B B1. (a) Explain the meaning of the following terms: (i) An extensive and an intensive thermodynamic property. [10%] (ii) An open and a closed system. [10%]

(b)

Describe the zeroth law of thermodynamics and explain briefly how the concept of temperature arises from the zeroth law. [20%] Air, which may be treated as an ideal gas, is contained within a leak proof vessel and has a mass of 3 kg. The air undergoes two thermodynamic processes (during which changes in kinetic and potential energy may be neglected): Isothermal expansion: from state 1, defined by V1  1 m 3 , to state 2 defined by p2  3 bar and V2  1.5 m 3 . from state 2 to state 3, defined by V3  1 m 3 .

(c)

Isobaric Compression:

(i) (ii) (iii) (iv)

Sketch the two processes on a p-V diagram. Calculate the pressure of the air at state 1. Calculate the temperature of the air at state 1.

[10%] [10%] [10%]

Calculate the overall work done by the air when going from state 1 to state 3. [25%] Calculate the heat transfer going from state 1 to state 2. [5%]

(v)

DATA Specific gas constant for air R = 0.287 kJ/kg K.

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B2. (a) Write down the steady flow energy equation. Stating any assumptions made, apply this equation to: (vi) (vii) a boiler a nozzle. [30%] (b) The power output from an adiabatic steam turbine is measured to be 5 MW. Steam enters the turbine as superheated vapour with a pressure p1  2 MPa , a temperature T1  400  C , a velocity c1  50 m/s and an elevation z1  10 m (see Figure QB2). At the exit from the turbine a wet vapour mixture is present and this has a dryness fraction of x2  0.9 , a pressure of p2  25 kPa , a velocity of c2  180 m/s and an elevation of z 2  6 m . Calculate: (i) the change in specific kinetic energy across the turbine, [10%] (ii) the change in specific potential energy across the turbine, [10%] (iii) the change in specific enthalpy across the turbine, [20%] (iv) the work done per unit mass of steam flowing through the turbine, [20%] (v) the mass flow rate of the steam. [10%]

p1 = 2 MPa T1 = 400 °C c1 = 50 m/s z1 = 10 m Turbine

 W p2 = 25 kPa x2 = 0.9 c2 = 180 m/s z2 = 6 m Figure QB2. Steam turbine.

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B3. (a) Describe, with an appropriate sketch on a p-v diagram, the phase changes which occur when a liquid such as water is expanded at constant temperature. Indicate clearly the phase change boundaries. [Include in your discussion references to wet vapour, dryness fraction and critical point]. [40%] A rigid industrial pressure vessel has an internal volume of 2 m3 and contains H2O in its wet vapour phase at a pressure of 2.7 bar and a dryness fraction of 0.236. Calculate: (i) (ii) (c) the specific volume of the wet vapour the mass of H2O present in the vessel. [15%] [5%]

(b)

The pressure vessel studied in part (b) is fitted with a safety valve which will blow at 20 bar. Calculate, (i) the temperature of the H2O when the valve blows, [10%] (ii) the heat that must be transferred into the pressure vessel in order to blow the valve. [30%]

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B4. (a) Describe in detail, and explain the differences between, three different mechanisms of heat transfer. [40%] Define what is meant by the term "black body". What properties does a black body possess? [20%] Air, at a temperature of 20 ºC, blows over a hot steel plate. The steel plate is 0.5 m wide and 1 m long, and the surface of this plate is maintained at 250 ºC. (i) If the convection heat transfer coefficient for this process is measured to be 25 W/m2 K, calculate the rate of convection heat transfer from the surface of the plate. [10%] If the emissivity of the steel plate is   0.72 , calculate the radiation heat transfer from the surface of the plate. [10%] (iii) If the steel plate is 20 mm thick, calculate the temperature of the plate on its inside surface, [20%]

(b)

(c)

(ii)

DATA Stefan Boltzmann Constant Thermal Conductivity of steel plate

  5.67 108 W/m2 K 4 k  43 W/m K

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