External Problem 1: Dimensional analysis and similarity A fighter aireraft is to operate at 200 m/s in air at standard conditions (p= 1.2 kg/m³). A model is constructed to 1/20 scale (length ratio) and tested in a wind tunnel at the same air temperature (same air viscosity) to determine the drag force. The drag force Fp is a function of the air density p and viscosity 4, the velocity V and the cross section length of the airplane D. a) Use dimensional analysis to prove that: F and , = pVD What are these two dimensionless numbers? b) If the model is tested at 50 m/s, what air density should be used in the wind tunnel? Comment the result and give a recommendation. c) If the model drag force is 250 N at 50 m/s, what will be the drag force of the prototype? Lift force 200 m/s Drag force
External Problem 1: Dimensional analysis and similarity A fighter aireraft is to operate at 200 m/s in air at standard conditions (p= 1.2 kg/m³). A model is constructed to 1/20 scale (length ratio) and tested in a wind tunnel at the same air temperature (same air viscosity) to determine the drag force. The drag force Fp is a function of the air density p and viscosity 4, the velocity V and the cross section length of the airplane D. a) Use dimensional analysis to prove that: F and , = pVD What are these two dimensionless numbers? b) If the model is tested at 50 m/s, what air density should be used in the wind tunnel? Comment the result and give a recommendation. c) If the model drag force is 250 N at 50 m/s, what will be the drag force of the prototype? Lift force 200 m/s Drag force
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...
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![15:39
Given-Assign..
External Problem 1: Dimensional analysis and similarity
A fighter aircraft is to operate at 200 m/s in air at standard conditions (p= 1.2 kg/m³). A
model is constructed to 1/20 scale (length ratio) and tested in a wind tunnel at the same
air temperature (same air viscosity) to determine the drag force. The drag force Fp is a
function of the air density p and viscosity u, the velocity V and the cross section length of
the airplane D.
a) Use dimensional analysis to prove that:
F
pVD?
and r, =
pVD
What are these two dimensionless numbers?
b) If the model is tested at 50 m/s, what air density should be used in the wind
tunnel? Comment the result and give a recommendation.
c) If the model drag force is 250 N at 50 m/s, what will be the drag force of the
prototype?
Lift force
200 m/s
Drag force
External Problem 2: Dimensional analysis and similarity
The viscous torque T produced on a disc rotating in a liquid depends upon the
characteristic dimension D, the rotational speed N, the density pand the dynamic
viscosity u](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf77a889-05ee-47fb-b1ee-62ea44a40fed%2Faf452dc0-64ea-4a0f-879b-c72d357bfd25%2Fawozldp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:15:39
Given-Assign..
External Problem 1: Dimensional analysis and similarity
A fighter aircraft is to operate at 200 m/s in air at standard conditions (p= 1.2 kg/m³). A
model is constructed to 1/20 scale (length ratio) and tested in a wind tunnel at the same
air temperature (same air viscosity) to determine the drag force. The drag force Fp is a
function of the air density p and viscosity u, the velocity V and the cross section length of
the airplane D.
a) Use dimensional analysis to prove that:
F
pVD?
and r, =
pVD
What are these two dimensionless numbers?
b) If the model is tested at 50 m/s, what air density should be used in the wind
tunnel? Comment the result and give a recommendation.
c) If the model drag force is 250 N at 50 m/s, what will be the drag force of the
prototype?
Lift force
200 m/s
Drag force
External Problem 2: Dimensional analysis and similarity
The viscous torque T produced on a disc rotating in a liquid depends upon the
characteristic dimension D, the rotational speed N, the density pand the dynamic
viscosity u
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