1. Consider a new wind tunnel to test and utilise the effects of boundary layer conditions in order to maintain the velocity of a fluid. Laminar airflow enters a square duct design through a 0.25m? opening, as is shown in Figure 1. Because the boundary layer displacement thickness increases in the direction of flow, it is necessary to increase the cross-sectional size of the duct if a constant U=1 m/s velocity to be maintained outside the boundary layer. Assume standard air temperature in the calculation. U = 1 m/s 0.25 m² d(x) 1 m/s Figure 1 a) Determine the expression of the duct size, d, in consideration to maintain the velocity outside the boundary layer. b) Plot a graph of the duct size, d, as a function of x for 0

1. Consider a new wind tunnel to test and utilise the effects of boundary layer conditions in order to maintain the velocity of a fluid. Laminar airflow enters a square duct design through a 0.25m? opening, as is shown in Figure 1. Because the boundary layer displacement thickness increases in the direction of flow, it is necessary to increase the cross-sectional size of the duct if a constant U=1 m/s velocity to be maintained outside the boundary layer. Assume standard air temperature in the calculation. U = 1 m/s 0.25 m² d(x) 1 m/s Figure 1 a) Determine the expression of the duct size, d, in consideration to maintain the velocity outside the boundary layer. b) Plot a graph of the duct size, d, as a function of x for 0

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 5.6P: 5.6 A fluid flows at 5 over a wide, flat plate 15 cm long. For each from the following list,...

See similar textbooks

Similar questions

5.6 A fluid flows at 5 over a wide, flat plate 15 cm long. For each from the following list, calculate the Reynolds number at the downstream end of the plate. Indicate whether the flow at that point is laminar, transition, or turbulent. Assume all fluids are at 40°C. (a) air, (b) , (c) water, (d) engine oil.
Air at 20C flows at 1 m/s between two parallel flat plates spaced 5 cm apart. Estimate the distance from the entrance to the point at which the hydrodynamic boundary layers meet.
A wind tunnel has a cross-section of 1.0m at its inlet by 1.0m and length 10m. Wind at uniform velocity 15m/s enters the tunnel at 20°C. Assume, velocity distribution in turbulent 1/5 y boundary layer to follow the law U (Kinematic viscosity= 1.53x10°m² /s) Assuming the boundary layer to be turbulent from the beginning, then the value of 8(represents in law) is calculated as
Consider laminar flow entering a tube. Before the fluid enters, the velocity profile is constant and equal to to. The tube diameter is D and radius R. You are interested in estimating how much distance the fluid must travel into the tube before the classic Poiseuille parabolic velocity profile is established - this distance is called the "entrance length" or Zent- Using boundary layer theory, which of the following would be a reasonable estimate? (Hint: assume as flow enters the tube, you can model the growing viscous boundary layer as laminar flow over a flat plate, and note that the De where v = Reynolds number for a tube is Rep %3D Zent = (Rep) Zent = D 2 (Rep) Zent = 2. Rep - Rep O Zent R-Rep %3D O None of the above.
Engine oil at 100°C flows on the top surface of a 1-m-long flat plate maintained at 20°C. The oil’s freestream speed (u infinity) is 0.1 m/s. Find the engine oil properties from the table A.5 A. Evaluate the Reynolds number, local convection coefficient, heat flux and shear stress at the end of the plate (x = L). Is the air flow laminar or turbulent over the plate?B. Evaluate the average convection coefficient, average heat flux, average shear stress and drag force over the plate.
(b) In two dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = ở. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. C5 Table 2: Equation of Velocity Profile Setting Equation wU = 2y/8 - (y/S² 1
8- Air (p = 1.21 kg/m') flows over a thin flat plate 1 m long and 0.3 m wide. The flow is uniform at the leading edge of the plate. Assume the velocity profile in the boundary layer is linear, and the free stream velocity is 2.7 m/s. Using control volume (abcd) shown in figure, compute the mass flow rate across surface (ab). Determine the magnitude and direction of the x- component of the force required to hold plate stationary. [3.9x10 kg/s ; -3.5×10* N]
Air flows inside a tube 60 mm in diameter (d) and 2.1 m long (l) at a velocity w = 5 m/sec. Find the heat-transfer coefficient α if the mean air temperature tf = 100oC. Note: Write your answer in space provided without the unit (the answer is in kcal/m2-hr-oC, one decimal places)
What are the physical and quantitative evidence of turbulence in fluid flow?
Cooling water for a power plant is stored in a pond 900 m in length and 400 m wide. A dry wind at 300 K blows in a horizontal direction parallel to the 900 m side of the pond at a velocity of 2 m/s. The cooling water is at 300 K. Known the air dynamic viscosity v= 1.67 x10m?/s.; the Re transition from laminar flow to turbulent flow is 500,000; and the saturated water vapor pressure at 300 K is 3580 Pa; gas constant R= 8.3144 J/mole.K. 1.) At what position across the pond is the air flow no longer laminar? Would it reasonable to assume that the mean gas-film mass transfer coefficient for water vapor in air is dominated by turbulent flow mass transfer? 2.) As part of an engineering analysis to predict the evaporation rate of water from the pond, determine the mean gas film mass transfer co-efficient. 3.) Calculate the rate of water evaporation from the pond.
(b) In two-dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reaches the value of zero at y = 8. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. Table 2: Equation of Velocity Profile Equation u/U = 3(y/8)/2 – (y/8)³/2 Setting 2
(b) In two-dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = 8. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. Table 2: Equation of Velocity Profile Equation u/U = 3(y/S)/2 – (y/8)³/2