Problem 6. A boundary layer is developing for uniform flow of air at STP over a flat plate as shown. The free- stream flow outside the boundary layer has an undisturbed velocity of U = 50 m/s. The plate has a width of b = 3.0 m perpendicular to the schematic. A control volume (CV) with control surfaces (ab), (bc), (cd), and (ad) is defined as shown. Assume that the flow in the boundary layer is turbulent at surface (cd) with a 1/7th power-law velocity profile and a boundary layer disturbance thickness of = 2.0 cm. For surfaces (ab), (bc), and (cd), calculate (a) mass flowrate and (b) momentum transported (in Newtons). (c) Determine the drag for the flat plate at surface (ad). y U control volume boundary-layer region a flat plate d U δ u(y)

Problem 6. A boundary layer is developing for uniform flow of air at STP over a flat plate as shown. The free- stream flow outside the boundary layer has an undisturbed velocity of U = 50 m/s. The plate has a width of b = 3.0 m perpendicular to the schematic. A control volume (CV) with control surfaces (ab), (bc), (cd), and (ad) is defined as shown. Assume that the flow in the boundary layer is turbulent at surface (cd) with a 1/7th power-law velocity profile and a boundary layer disturbance thickness of = 2.0 cm. For surfaces (ab), (bc), and (cd), calculate (a) mass flowrate and (b) momentum transported (in Newtons). (c) Determine the drag for the flat plate at surface (ad). y U control volume boundary-layer region a flat plate d U δ u(y)

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 5.24P: Engine oil at 100C flows over and parallel to a flat surface at a velocity of 3 m/s. Calculate the...

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Engine oil at 100C flows over and parallel to a flat surface at a velocity of 3 m/s. Calculate the thickness of the hydrodynamic boundary layer at a distance 0.3 m from the leading edge of the surface.
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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…
Problem 6. A boundary layer is developing for uniform flow of air at STP over a flat plate as shown. The free-stream flow outside the boundary layer has an undisturbed velocity of U = 50 m/s. The plate has a width of b = 3.0 m perpendicular to the schematic. A control volume (CV) with control surfaces (ab), (bc), (cd), and (ad) is defined as shown. Assume that the flow in the boundary layer is turbulent at surface (cd) with a 1/7th power-law velocity profile and a boundary layer disturbance thickness of 8 = 2.0 cm. For surfaces (ab), (bc), and (cd), calculate (a) mass flowrate and (b) momentum transported (in Newtons). (c) Determine the drag for the flat plate at surface (ad). U U control volume u(y) boundary-layer region flat plate a
Problem-2 For the turbulent incompressible boundary layer, the velocity profile is given as u/Ue, y = y/8, Ue and d are boundary-layer edge velocity where, u = and boundary layer thickness, respectively. Using momentum integral equation, prove that: 8/x = 0.383/Re,/5 8% /x = 0.0479/Re/5 and 0/x = 0.0372/Re/5
A two-dimensional diverging duct is being designed to diffuse the high-speed air exiting a wind tunnel. The x-axis is the centerline of the duct (it is symmetric about the x-axis), and the top and bottom walls are to be curved in such a way that the axial wind speed u decreases approximately linearly from u1 = 300 m/s at section 1 to u2 = 100 m/s at section 2 . Meanwhile, the air density ? is to increase approximately linearly from ?1 = 0.85 kg/m3 at section 1 to ?2 = 1.2 kg/m3 at section 2. The diverging duct is 2.0 m long and is 1.60 m high at section 1 (only the upper half is sketched in Fig. P9–36; the halfheight at section 1 is 0.80 m). (a) Predict the y-component of velocity, ?(x, y), in the duct. (b) Plot the approximate shape of the duct, ignoring friction on the walls. (c) What should be the half-height of the duct at section 2?
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