A fluid Prandti number Pr=1 at 500K flows over a plate of 2.5 m length, maintained at 300K. The velocity of the fluid is 20m/s. Assuming kinematic viscosity v= 20*10^-6 m2/s. Determine the thermai boundary layer thickness at 0.6 m from the leading edge ?
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- 1. A fluid is bounded by two parallel plates of infinite width and length as shown in FIGURE Q1. The upper plate moves at 7 m/s, and the lower plate is fixed. The fluid's dynamic viscosity is 1.85X105 N.s/m?. Assume Couette flow with pressure gradient, = 0.1 N/m³. a. Propose the discretization method to solve Couette flow equation with pressure gradient below. Let the number of nodes, n = 9, the distance between the nodes is 0.05 m. Obtain the velocity of all the internal nodes using the matrix inversion method and the iterative method. Compare the results and the effectiveness of both methods (in terms of calculation effort and ease of setting up the problem). + b. Flow shear stress is governed by the following equation ôu Propose the discretization method to solve the above equation and calculate the shear stress at node 1. Describe the condition in tems of the pressure gradient when the shear stress at the bottom plate is zero. Moving plate at Um/s N= N-1 `Fixed plate FIGURE Q1An isothermal long cylinder with square (side of 0.4 m and diagonal of 0.5657 m) cross-section is placed in a flow with a velocity of 1 m/s as shown. The properties of the fluid are: kinematic viscosity is 1.38 x 10-5 m²/s, thermal conductivity is 0.024 W/m.°C, and Prandtl number is 0.73. What is the average Nusselt number for the flow? 1253 a Figure 1: Flow configuration for Problem 6. The dimensions are: a=0.4 m, b=0.5657 mA fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at 300 K. The velocity of the fluid is 10 m/s. Assuming kinetic viscosity, v = 30 x 10-6 m²/s, the thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is (up to three decimal)?
- 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.A plate is cooled by a fluid with Prandtl number Pr >> 1. Surface temperature varies with distance form the leading edge according to where C is constant. For such a fluid it is reasonable to assume that axial velocity within the thermal boundary layer is linear given by u=V% y Determine the local Nusselt number and show that surface heat flux is uniform. Use a third degree polynomial temperature profile and assume laminar boundary layer flow y YA To Vo T₁(x,0)=T +C√√x U -8 &₁ X T₁(x) = T₁ +C√xA cube of side (a) and mass (M) is initially sitting fully submerged at the bottom of a container filled with a liquid of kinematic viscosity v and density p. The container has a square cross-section of side (a+a/5) and the cube is sitting right at the middle of the container base. (a) A force (F) starts pulling the cube up at a constant velocity (U). Develop an expression for the force in terms of (U, M. a. g, p and v). You may assume that the velocity in the gap between the cube's sides and the container walls is linear. The expression for (F) is to be valid as long as the cube remains submerged. (b) After the cube reaches the water surface, it continues to be pulled up by the same force. Develop a differential equation for the variation with time of the fraction of the cube that is submerged in water.
- Extend the steady fl ow between a fi xed lower plate and amoving upper plate, to the case of twoimmiscible liquids between the plates, as in Fig. (a) Sketch the expected no-slip velocity distribution u ( y )between the plates. ( b ) Find an analytic expression for thevelocity U at the interface between the two liquid layers.( c ) What is the result of ( b ) if the viscosities and layerthicknesses are equal?The erythrocyte sedimentation rate (heaviness) test of a blood sample is often used as a diagnosis of immune disorders and some other diseases. Assuming that the red blood cells are about a sphere with a diameter of (approximately 5 um) and a density (g/ml 1.125), and the density and viscosity of the plasma in which the red blood cells are settled (Pa.s), (1025 kg/m3 10-3 x 1.5) On arrangement and acceleration m/s2 9.81 Calculate the erythrocyte sedimentation rate (settlement rate). 9:40 73% * "l Asiacell 90 x 10-6 m/s 1 0.9 x 10-6 m/min 90 x 10-6 m/minA cubic block of side L and mass M is dragged over an oil film across table by a string connects to a hanging block of massmas shown in figure. The Newtonian oil film of thickness h has dynamic viscosity u and the flow condition is laminar. The acceleration due to gravity is g. The steady state velocity V of block is M Mgh (a) Mgh (b) mgh (c) mgh (d)
- 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.Air is flowing naturally over a cylinder of D=(1) cm. Air has thermal conductivity 0.027W/mK, kinematic viscosity 1.9*10-5 m2/s, Rayleigh number 108, and Prandtl number0.72. Find the Nusselt number uses charts/table also if neededProve Navier Stokes equation for incompressible fluids