Flight Dynamics Problems and solution - part 1

Flight Dynamics Problems and solution - part 1
[Useful for GATE - AEROSPACE ENGINEERING (AE )]

An aircraft cruises at a calibrated airspeed of 320 kt in FL 200. The outside air temperature is -23 °C. a) Calculate the air pressure p in FL 200.
b) Calculate the air density r in FL 200 under given conditions.
c) Determine the equivalent airspeed EAS from a suitable diagram.
d) Calculate the equivalent airspeed EAS.
e) Calculate the true airspeed TAS.
f) Calculate the Mach number.

An aircraft is equipped with a wing of symmetrical airfoils:-

During an IFR flight, a passenger looks out the window while relaxing in his seat. He observes a turn and estimates the bank angle to be 30°. At the same time, the passenger observes the free surface of the orange juice in his glass: it is parallel to the tray.
a) The passenger assumes the turn being flown as a rate one turn. Explain the term rate one turn. Why is it correct to assume a rate one turn.
b) The passenger assumes the turn being flown as a coordinated turn. Explain the term coordinated turn. Why is it correct to assume a coordinated turn.
c) Calculate the aircraft's true airspeed

An aerobatic airplane flies a perfect circular looping. The pilot reads an altitude of 5000 ft at the highest point of the looping and an altitude of 4000 ft a the lowest point of the looping. The looping is flown at such a speed that the lowest load factor in the looping is n = 0. Assume that aircraft speed is nearly constant in the looping. a) During which part of the looping does the airplane experience the highest load factor? b) What is the aircraft's speed in the looping? c) Calculate the highest load factor n during the looping.

A jet cruises with constant lift coefficient and constant Mach number of 0.82 in the stratosphere. The take-off mass with full fuel tanks is 271000 kg, the maximum fuel volume is 135000 liters, fuel density is 800 kg/m³. The specific fuel consumption is 16 mg/(Ns). The aircraft has a specified range of 7200 NM.
a) Write down the appropriate equation for these flight conditions from which the range can be calculated. How is this equation named?
b) Calculate the aircraft's mass without fuel.
c) On its fuel reserves, the aircraft could fly additional 920 NM plus further 30 min. How far could the aircraft fly in these 30 min. if we assume that the 30 min. are also flown at cruise speed? How far could the aircraft fly on its fuel reserves?
d) Calculate the aircraft's lift-to-drag ratio.

Derive an equation for the range of a jet aircraft in a (shallow) steady climb with constant airspeed and constant lift coefficient.

GATE Aerospace Engg Tutorial Part - 2

GATE Aerospace Engg Tutorial Part-1

Fluid Mechanics Competitive Q & A [ISRO ,DRDO, Ph.D RET, GATE] - PART1

Which of the following is an example of laminar flow? A. Under ground flow B. Flow past tiny bodies C. Flow of oil in measuring instruments D. all of these Answer & Explanation Answer: Option D In one dimensional flow, the flow

A. is steady and uniform B. takes place in straight line C. takes place in curve D. takes place in one direction Answer & Explanation Answer: Option B

A flow whose streamline is represented by a curve, is called

A. one-dimensional flow B. two-dimensional flow C. three-dimensional flow D. four-dimensional flow Answer & Explanation Answer: Option B

The imaginary line drawn in the fluid in such a way that the tangent to any point gives the direction of motion at that point, is known as

A. path line B. stream line C. steak line D. potential line Answer & Explanation Answer: Option B

The tangential velocity of the water element having a free vortex is A. directly proportional to its distance from the centre B. inversely proportional to its distance from the centre C. directly proportional to its (distance)2 from the centre D. inversely proportional to its (distance)2 from the centre Answer & Explanation Answer: Option B The kinematic viscosity is the

A. ratio of absolute viscosity to the density of the liquid B. ratio of density of the liquid to the absolute viscosity C. product of absolute viscosity and density of the liquid D. product of absolute viscosity and mass of the liquid Answer & Explanation Answer: Option A

When a body is placed over a liquid, it will float if A. gravitational force is equal to the upthrust of the liquid B. gravitational force is less than the upthrust of the liquid C. gravitational force is more than the upthrust of the liquid D. none of the above Answer & Explanation Answer: Option B When a body is placed over a liquid, it will sink down if A. gravitational force is equal to the upthrust of the liquid B. gravitational force is less than the upthrust of the liquid C. gravitational force is more than the upthrust of the liquid D. none of the above Answer & Explanation Answer: Option C The buoyancy depends upon the A. weight of the liquid displaced B. pressure with which the liquid is displaced C. viscosity of the liquid D. compressibility of the liquid Answer & Explanation Answer: Option A The length AB of a pipe ABC in which the liquid is flowing has diameter (d1) and is suddenly enlarged to diameter (d2) at B which is constant for the length BC. The loss of head due to sudden enlargement is

A. B. C. D. Answer & Explanation Answer: Option C

Coefficient of contraction is the ratio of

A. actual velocity of jet at vena contracta to the theoretical velocity B. loss of head in the orifice to the head of water available at the exit of the orifice C. actual discharge through an orifice to the theoretical discharge D. area of jet at vena contracta to the area of orifice Answer & Explanation Answer: Option D

Coefficient of resistance is the ratio of

A. actual velocity of jet at vena contracta to the theoretical velocity B. area of jet at vena contracta to the area of orifice C. loss of head in the orifice to the head of water available at the exit of the orifice D. actual discharge through an orifice to the dieoretical discharge Answer & Explanation Answer: Option C

The power transmitted through the pipe is maximum when the head lost due to friction is equal to A. one-fourth of the total supply head B. one-third of the total supply head C. one-half of the total supply head D. two-third of the total supply head Answer & Explanation Answer: Option B In order to measure the flow with a venturimeter, it is installed in

A. horizontal line B. inclined line with flow upwards C. inclined line with flow downwards D. any direction and in any location Answer & Explanation Answer: Option D

The loss of head due to friction in a pipe of uniform diameter in which a viscous flow is taking place, is (where RN = Reynold number)

A. 1/RN B. 4/RN C. 16/RN D. 64/RN Answer & Explanation Answer: Option C

The liquid used in manometers should have

A. low density B. high density C. low surface tension D. high surface tension Answer & Explanation Answer: Option D

A manometer is used to measure

A. low pressure B. moderate pressure C. high pressure D. atomospheric pressure Answer & Explanation Answer: Option C

The body will sink down if the force of buoyancy is __________ the weight of the liquid displaced.

A. equal to B. less than C. more than Answer & Explanation Answer: Option B

The velocity corresponding to Reynold number of 2000 is called

A. sub-sonic velocity B. super-sonic velocity C. lower critical velocity D. higher critical velocity Answer & Explanation Answer: Option C

The velocity corresponding to Reynold number of 2800, is called

A. sub-sonic velocity B. super-sonic velocity C. lower critical velocity D. higher critical velocity Answer & Explanation Answer: Option D

The atmospheric pressure at sea level is

A. 103 kN/m2 B. 10.3 m of water C. 760 mm of mercury D. all of these Answer & Explanation Answer: Option D

The loss of pressure head in case of laminar flow is proportional to

A. velocity B. (velocity)2 C. (velocity)3 D. (velocity)4 Answer & Explanation Answer: Option A

The flow of water through the hole in the bottom of a wash basin is an example of

A. steady flow B. uniform flow C. free vortex D. forced vortex Answer & Explanation Answer: Option C

The velocity at which the laminar flow stops, is known as

A. velocity of approach B. lower critical velocity C. higher critical velocity D. none of these Answer & Explanation Answer: Option B

When a cylindrical vessel, containing some liquid, is rotated about its vertical axis, the liquid surface is depressed down at the axis of its rotation and rises up near the walls of the vessel on all sides. This type of flow is known as

A. steady flow B. turbulent flow C. vortex flow D. uniform flow Answer & Explanation Answer: Option C

The shear stress-strain graph for a newtonian fluid is a

A. straight line B. parabolic curve C. hyperbolic curve D. elliptical Answer & Explanation Answer: Option A

A flow in which the viscosity of fluid is dominating over the inertia force is called

A. steady flow B. unsteady flow C. laminar flow D. turbulent flow Answer & Explanation Answer: Option C

The length of the divergent cone in a venturimeter is __________ that of the convergent cone.

A. equal to B. double C. three to four times D. five to six times Answer & Explanation Answer: Option C

A flow through a long pipe at constant rate is called

A. steady uniform flow B. steady non-uniform flow C. unsteady uniform flow D. unsteady non-uniform flow Answer & Explanation Answer: Option A

With an increase in size of tube, the rise or depression of liquid in the tube due to surface tension will

A. decrease B. increase C. remain unchanged D. depend upon the characteristics of liquid Answer & Explanation Answer: Option A

The hammer blow in pipes occurs when

A. there is excessive leakage in the pipe B. the pipe bursts under high pressure of fluid C. the flow of fluid through the pipe is suddenly brought to rest by closing of the valve D. the flow of fluid through the pipe is gradually brought to rest by closing of the valve Answer & Explanation Answer: Option C