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Flat Plate, Water. Water flows at atmospheric pressure over a flat plate at U = 5m/s. (a) At what distance x* from the leading edge will the flow become turbulent? (b) At x*, assuming laminar flow, what is the (i) boundary layer thickness 8*, (ii) the wall shear stress and (iii) the speed ratios u/U and v/U at y = 8*/2? (c) If a pitot tube, open at the top, is placed at y = 8*/2 and fills with water, what is the pitot manometer height, h (assume Pg = 0 in the boundary layer)? Ans OM: (a) x*: 10-¹ m; (b) 8*: 104 m, Tw: 10¹ Pa, u/U: 10-¹, v/U: 104; (c) h: 10¹ m.

Flat Plate, Water. Water flows at atmospheric pressure over a flat plate at U = 5m/s. (a) At what distance x* from the leading edge will the flow become turbulent? (b) At x*, assuming laminar flow, what is the (i) boundary layer thickness 8*, (ii) the wall shear stress and (iii) the speed ratios u/U and v/U at y = 8*/2? (c) If a pitot tube, open at the top, is placed at y = 8*/2 and fills with water, what is the pitot manometer height, h (assume Pg = 0 in the boundary layer)? Ans OM: (a) x*: 10-¹ m; (b) 8*: 104 m, Tw: 10¹ Pa, u/U: 10-¹, v/U: 104; (c) h: 10¹ m.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
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.
Chapter6: Forced Convection Over Exterior Surfaces
Section: Chapter Questions
Problem 6.34P
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Assume Patm = 10^5, Pa = 14.7 psi ; pwater ~ 1000 kg/m3; pair ~ 1.2 kg/m3; μwater ~ 10^-3 N•s/m2; µair ~ 2 x 10^-5 N•s/m2; Vwater ~ 10^-6 m2 /s ; Vair ~ 1.67 x 10^-5 m2/s ; g = 9.8 m/s^2 .; 1 m/s = 2.24 mph ; 1lbf = 4.45 N ; 1 m^3 = 264 gallons Changing variables, the IBL eq'n 9.21 can be written as: TW = pU^2 (d8/dx) [ S(u/U)(1-u/U)dn] where n = y/6, with integral limits 0 to 1. Assuming profiles of the form u/U = f(n) then the integral value is a pure number. Again, for turbulent IBL we set TW = 0.0233 pU^2 [v/(U8)]^(1/4) on LHS Flat Plate, Water. Water flows at atmospheric pressure over a flat plate at U = 5m/s. (a) At what distance x* from the leading edge will the flow become turbulent? (b) At x*, assuming laminar flow, what is the (i) boundary layer thickness 8*, (ii) the wall shear stress and (iii) the speed ratios u/U and v/U at y = 8*/2? (c) If a pitot tube, open at the top, is placed at y = 8*/2 and fills with water, what is the pitot manometer height, h (assume Pg = 0 in the boundary layer)? Ans OM: (a) x*: 10-¹ m; (b) 8*: 104 m, tw: 10¹ Pa, u/U: 10¹¹, v/U: 104; (c) h: 10¹¹ m.
Transcribed Image Text:Assume Patm = 10^5, Pa = 14.7 psi ; pwater ~ 1000 kg/m3; pair ~ 1.2 kg/m3; μwater ~ 10^-3 N•s/m2; µair ~ 2 x 10^-5 N•s/m2; Vwater ~ 10^-6 m2 /s ; Vair ~ 1.67 x 10^-5 m2/s ; g = 9.8 m/s^2 .; 1 m/s = 2.24 mph ; 1lbf = 4.45 N ; 1 m^3 = 264 gallons Changing variables, the IBL eq'n 9.21 can be written as: TW = pU^2 (d8/dx) [ S(u/U)(1-u/U)dn] where n = y/6, with integral limits 0 to 1. Assuming profiles of the form u/U = f(n) then the integral value is a pure number. Again, for turbulent IBL we set TW = 0.0233 pU^2 [v/(U8)]^(1/4) on LHS Flat Plate, Water. Water flows at atmospheric pressure over a flat plate at U = 5m/s. (a) At what distance x* from the leading edge will the flow become turbulent? (b) At x*, assuming laminar flow, what is the (i) boundary layer thickness 8*, (ii) the wall shear stress and (iii) the speed ratios u/U and v/U at y = 8*/2? (c) If a pitot tube, open at the top, is placed at y = 8*/2 and fills with water, what is the pitot manometer height, h (assume Pg = 0 in the boundary layer)? Ans OM: (a) x*: 10-¹ m; (b) 8*: 104 m, tw: 10¹ Pa, u/U: 10¹¹, v/U: 104; (c) h: 10¹¹ m.
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