Subject Code:2171914
GUJARAT TECHNOLOGICAL UNIVERSITY
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BE- SEMESTER-VII (NEW) EXAMINATION - WINTER 2020
Subject Name:Gas Dynamics
Time:10:30 AM TO 12:30 PM
Instructions:
- Attempt any FOUR questions out of EIGHT questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
- Use of Gas Table is permitted.
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Q.1 (a) Define following :
- Crocco number
- Mach number
- Stagnation enthalpy
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(b) Define bulk modulus of elasticity and derive its equation for isothermal process.
(c) Define M*. Derive following relation:
M2 = { }M*2
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Calculate its maximum value for diatomic gas.
Q.2 (a) Compare adiabatic expansion and isentropic expansion processes on T—>S diagram.
(b) An air jet at 400K has sonic velocity. Calculate
- velocity of sound at the stagnation condition and
- Maximum possible velocity of jet
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Take : R =287 J/kg-K and ? = 1.4.
(c) From the continuity equation, derive the equation for non-dimensional mass flow rate in terms of pressure ratio of static and stagnation pressure.
Non-dimensional mass flow rate =
Q.3 (a) What is shock strength?.Write the equation which represents shock strength in terms of upstream Mach number.
(b) A gas at a Mach number of 1.8, pressure 0.8 bar and temperature 373K passes through a normal shock wave. Determine density after the shock. Compare its value in an isentropic compression through same pressure ratio. Take: R =287 J/kg-K and ? = 1.4.
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(c) Starting from energy equation prove that,
M1*M2 = 1.
Where upstream and downstream reference Mach numbers for normal shock are represented by M1* and M2 respectively.
Q.4 (a) What is shock? Represent normal shock on h->s diagram along with Rayleigh and Fanno curve.
(b) Condition of gas at upstream side of shock:
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M=2.5 p=2 bar and T = 275K.
(c) From the energy equation, derive the following relation for the normal shock
Where upstream and downstream reference Mach numbers for normal shock are represented by Mx" and M’y respectively.
Q.5 (a) What is Fanno flow? State assumptions related to Fanno flow process.
(b) Prove that at maximum entropy point on Fanno curve is where Mach number is unity and all processes approach this point.
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(c) A circular duct passes 8.25 kg/s of air at an exit Mach number of 0.5. The entry condition of air is 3.45 bar and 311K. Co-efficient of friction of duct is 0.005. If entry Mach number is 0.15 determine:
- Length of duct
- Diameter of duct
- Exit pressure and temperature of air.
Q.6 (a) Differentiate : Fanno flow and Isothermal flow.
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(b) Write governing describing Fanno curve. Draw three different Fanno curve on T->S diagram for three different mass densities.
(c) Air at stagnation pressure 10 bar, stagnation temperature 400K and M = 3 is supplied to a 50mm diameter pipe. The friction factor for the pipe surface is 0.002. If exit Mach number is 1, calculate :
- The length of pipe
- Velocity of sound at entry
- Mass flow rate.
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Q.7 (a) What is critical state? Calculate the ratio of stagnation pressure to the critical pressure for monoatomic gas.
(b) State the four assumptions of Rayleigh flow as well as write two applications where Rayleigh flow analysis is applicable.
(c) A combustion chamber in a gas‘turbine plant receives air at 350K, 0.55bar and 75 m/s. The air-fuel ratio is 29 and calorific value of fuel is 41.87MJ /kg. For the gas determine :
- Initial and final' Mach number
- Final temperature and pressure of the gas.
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Take: R=287 J/kg-K and ? = 1.4.
Q.8 (a) Write the equation of A/A* and draw the graph of (A/A*) > M.
(b) Write momentum equation for Rayleigh flow. Plot Rayleigh curve on p>v diagram and find : (j—pj for Rayleigh line.
(c) Write momentum equation for Rayleigh flow and from that derive equations for (F/F*), (p/p*) and (po/po*)
Where F represents impulse function.
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Date:19/01/2021
Total Marks: 56
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