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- Q4) Define the boundary layer, then find the thickness of boundary layer, shear stress, drag force and coefficiet of drag in terms of Re for the velocity profile of laminar boundary layer u/U=4(y/8)-6(y/8)5. Calcate the boundary layer thickness and drag force if the air flows over a sharp edged flat plate 1m long and 0.5m wide at a velocity 0.9m/s, the air density 1.23 kg/m³ and the kinematic viscosity is 1.46*10-5 m/s².(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
- QI/ If the velocity profile of the boundary layer is 4 =-÷O find the thickness of boundary %3D layer, the shear stress at trailing edge and the drag force on one side of plate 2 m long , i if it is Kg immersed in water flowing with velocity of 0.4 m/s (p = 998 , 0= 1.007*10-6 m2/s m3(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 = 6. Based on Table 2 and setting given to you; () 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 Setting Equation wU = 3(y/8)/2 – (y/8j?/2B) for the velocity profiles given below, state whether the boundary layer has separated or on the verge of separation or will remain attached ( i) u/U=2(y/8) -(y/8)² ii) u/U=-2(y/8) +0.5(y/8)³ iii) u/U-1.5(y/8) +0.5(y/8)³ Q3: Find the displacement, momentum thickness and energy thickness for the velocity distribution in the boundary layer: F u/U=0.5(y/8) + 1.5(y/8)³ Q4: A) Find the velocity distribution and expression of the maximum velocity and shear stress for a flow between two stationary plates. C B) A laminar flow of oil between two horizontal fixed parallel plates with a maximum velocity 2 m/s and 100mm apart. Canulate the pressure gradient and shear stress. Take µ-2.4525 s/m².
- 1. The Stokes-Oseen formula for drag force Fon a sphere of diameter D in a fluid stream of low velocity V, density p, and viscosity u is: 9T F = 3TuDV + 16PD? Is this formula dimensionally homogenous? 2. The efficiency n of a pump is defined as the (dimensionless) ratio of the power required to drive a pump: QAp input power Where Q is the volume rate of flow and Ap is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure of Ibf/in? (1ft = 12 in) when its flow rate is 40 L/s (1L =0.001 m). If the input power is 16hp (1hp = 760 W), what is the efficiency?QI/ If the velocity profile of the boundary layer is :O find the thickness of boundary layer, the shear stress at trailing edge and the drag force on one side of plate 2 m long, if it is immersed in water flowing with velocity of 0.4 m/s (p 998 D = 1.007*10-6 m2/s %3DRederive Pouiseuelle’s Law for flow in a tube using the Navier-Stokes strategy. What are the boundary conditions you will use? (you can use a horizontal tube with no gravity at play and just small p, not script p)
- Q4:: Discuss the boundary layer development with the help of diagram by clearly illustrating different regions of flow. Also, discuss the steps used in solving boundary layer equationswrite Prandtl's boundary layer equation with appropriate boundary conditionsQuestion A3 a) With the help of sketches briefly describe the main differences between laminar and turbulent boundary layers in relation to friction drag and flow separation. A tug boat is pulling a log raft (Figure QA3) on the surface of a lake at a constant speed of Uboat = 5m/s. The log raft can be modelled as a flat plate (L=20m and W = 5.0m). u ug U boat 8 U Tug Boat rope boat Air Water L -X Log Raft Figure QA3 Assume the boundary layer forming on both sides (air side and water side) of the log raft is two-dimensional and laminar with a second order velocity distribution: W b) By using the Momentum Integral Equation find an expression for the wall shear stress in terms of Reynolds number and then estimate the tensile stress acting on the rope assuming the rope has a circular cross section with a diameter of 15 mm) and the power required to pull it. c) What would be the tensile stress on the rope if we assume the boundary layers on the log raft were turbulent? You may assume:…