For Air Assume: v=1.46×10 -5 m²/s and p = 1.225 kg/m³ Question A1 A flat plate with unit width is placed in a uniform steady two-dimensional flow of air with negligible pressure gradient. The velocity distribution of the boundary layer forming on either side of this plate has been given as: U/U8 = 2.0(y/ 8) - (y/8)2.0, where Us = 10 m/s. 1- Find and expression for the boundary layer thickness as a function of Rex. 2- At x=1.0 m calculate the shear stress corresponding to the points y=0.0,3.0 and 10.0 mm. 3- Calculate the boundary layer displacement and momentum thicknesses at x=1.0m. By using the calculated momentum thickness determine the drag force acting on one side of the plate between its leading edge and x = 1.0m. 4- At x=1.0m, calculate the mass flow rate through the boundary layer (mkg/s per unit width of the plate). What is the corresponding mass flow rate if the flow was inviscid (m; kg/s per unit width of the plate)? 5- By using appropriate equation (s) explain how the difference between mand mi can be related to the boundary layer displacement.

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Chapter5: Analysis Of Convection Heat Transfer
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PART A
-5
For Air Assume: v=1.46×10 m²/s and p =1.225 kg/m³
Question A1
A flat plate with unit width is placed in a uniform steady two-dimensional flow of air with
negligible pressure gradient. The velocity distribution of the boundary layer forming on
either side of this plate has been given as:
U /Us = 2.0(y/ 8) - (y/8)2.0, where U = 10 m/s.
1- Find and expression for the boundary layer thickness as a function of Rex.
2- At x=1.0 m calculate the shear stress corresponding to the points y=0.0,3.0 and
10.0 mm.
3- Calculate the boundary layer displacement and momentum thicknesses at
x=1.0m. By using the calculated momentum thickness determine the drag force
acting on one side of the plate between its leading edge and x = 1.0m.
4- At x=1.0m, calculate the mass flow rate through the boundary layer (mkg/s per
unit width of the plate). What is the corresponding mass flow rate if the flow was
inviscid (m; kg/s per unit width of the plate)?
5- By using appropriate equation (s) explain how the difference between mand m
can be related to the boundary layer displacement.
Question A2
a) Consider a steady, laminar flow through a straight horizontal tube having the
constant elliptical cross section given by the equation
x² 12
62
=1
Transcribed Image Text:PART A -5 For Air Assume: v=1.46×10 m²/s and p =1.225 kg/m³ Question A1 A flat plate with unit width is placed in a uniform steady two-dimensional flow of air with negligible pressure gradient. The velocity distribution of the boundary layer forming on either side of this plate has been given as: U /Us = 2.0(y/ 8) - (y/8)2.0, where U = 10 m/s. 1- Find and expression for the boundary layer thickness as a function of Rex. 2- At x=1.0 m calculate the shear stress corresponding to the points y=0.0,3.0 and 10.0 mm. 3- Calculate the boundary layer displacement and momentum thicknesses at x=1.0m. By using the calculated momentum thickness determine the drag force acting on one side of the plate between its leading edge and x = 1.0m. 4- At x=1.0m, calculate the mass flow rate through the boundary layer (mkg/s per unit width of the plate). What is the corresponding mass flow rate if the flow was inviscid (m; kg/s per unit width of the plate)? 5- By using appropriate equation (s) explain how the difference between mand m can be related to the boundary layer displacement. Question A2 a) Consider a steady, laminar flow through a straight horizontal tube having the constant elliptical cross section given by the equation x² 12 62 =1
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