GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-VII (NEW) EXAMINATION — WINTER 2017
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Subject Code: 2171914 Date: 02/11/2017Subject Name: Gas Dynamics(Department Elective - I)
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
- Use of gas table is permitted.
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MARKS
Q.1
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(a) Define : 1) Isothermal compressibility 03
2) Stagnation state
3) Critical velocity of sound.
(b) Define: Mach number. Show graphically that zone of silence is greater 04
than zone of action when object is moving with speed more than the
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velocity of sound.(c) What is M*? What is the advantage of using it instead of Mach number 07
? Derive the relation :
M2 = (?+1)M2 / (2 + (?-1)M2)
Q.2
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(a) Define critical state? Calculate the ratio of stagnation density to critical 03
density for monoatomic ideal gas.
(b) From continuity equation derive following equation for isentropic flow: 04
c = v(2?/(?-1)RT0{1- (p/p0)(?-1)/?})
(c) Air is discharged from a reservoir at P0 = 6.91 bar and 07
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T0 = 325°C through a nozzle to an exit pressure of 0.98 bar. If the flowrate is 3600 kg / hr determine for isentropic flow:
1) Throat area and throat pressure
2) Exit area and exit Mach number.
OR
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(c) A supersonic wind tunnel settling chamber expands air through a nozzle 07
from a pressure of 10 bar to 4 bar in the test section. Calculate the
stagnation temperature to be maintained in the settling chamber to
obtain a velocity of 500 m/s in the test section for air. What is the value
of Mach number at test section. Take : Cp = 1.025 kJ/ kg-K and Cv =
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0.735 kJ/ kg-K.Q.3
(a) What is shock wave? State the assumptions for studying normal shock 03
wave.
(b) Air enters a convergent-divergent nozzle with a pressure of 2.9MPa. 04
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When shock occurs pressure at upstream side is 0.5MPa. DetermineMach number and pressure at the downstream side of the shock.
(c) Derive the equation for ratio of downstream pressure to upstream 07
pressure in terms of upstream Mach number for normal shock.
OR
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Q.3 (a) What is the order of size of control volume to accommodate shock 03
(b) A compression shock wave occurs in a divergent air flow passage. On 04
the upstream side of the shock, the velocity of air is 400m/s,
temperature is 35°C and pressure 0.2 MPa. Find pressure and
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temperature at downstream side.(c) Derive Prandtl-Meyer equation for the normal shock in perfect gas. 07
Q.4
(a) State assumptions made in deriving equations for Fanno flow. State two 03
engineering fluid flow conditions which can be analyzed as Fanno flow.
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(b) From the adiabatic energy equation prove that irrespective of entry 04
condition of flow limiting condition at exit for Fanno flow is when M
=1.
(c) Air flows through an insulated circular pipe at a rate of 495 kg/min. The 07
pressure, temperature and Mach number at entrance to the pipe are
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0.3MPa, 27°C and 0.15 respectively. The co-efficient of friction of pipeis constant and its value is 0.005. If the Mach number at exit is 0.5,
Calculate
1) Diameter of pipe
2) Length of pipe
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3) Pressure at the exit of pipe.OR
Q.4 (a) What is Fanno flow? Write governing equations for Fanno flow. 03
(b) Draw h—>s and h>v curves for Fanno flow process for two different 04
mass flux. Here h ,s and v represent specific enthalpy, specific entropy
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and specific volume respectively.(c) The average friction factor of a 25mm diameter 12m long pipe is 0.004. 07
The condition of air at entry is 0.2Mpa, and 300K. Determine, Pressure,
Temperature and Mach number at exit. Consider sound velocity is four
times higher as compared to air velocity at inlet.
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Q.5
(a) Write equation of ‘T*A' Based on that show that to obtain accelerating 03
flow 1) Flow area should be increased in a supersonic flow and 2)
Flow area is decreased in subsonic flow.
(b) Enlist two flow situations where Rayleigh flow analysis is applicable. 04
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Represent Rayleigh flow' process on h = s diagram. Show locus ofstagnation enthalpy and Maximum entropy also.
(c) Represent Rayleigh'line on p - v diagram. Based on diagram show 07
that Mach number is 1/v? when enthalpy becomes maximum.
OR
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Q.5 (a) Draw Prandtl velocity ellipse and show different flow regimes on that. 03
(b) How the enthalpy changes in the Rayleigh flow when heat addition 04
continues beyond maximum enthalpy point?
(c) Derive the equations for P/P* and P0/P0* for Rayleigh flow. 07
Where P* is critical pressure and P0* is critical stagnation pressure.
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