In flow over a surface, velocity and temperature profiles are of the forms u(y) = Ay + By? + Cy3 and T(y) = D+ Ey + Fy2- Gy3 where the coefficients A through G are constants. Obtain expressions for the friction coefficient C, and the convection coefficient h in terms of uco, To, and appropriate profile coefficients and fluid pronerties
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- Example(1-13): steam and water flow through 75 mm inside diameter pipe at flow rate of 0.05 and 1.5 m³/s respectivily. If the mean temperature and pressure are 330 K and 120 kpa, what is the pressure drop per unit length of pipe. Where the pipe roughness 0.00015 mm, liquid and gas viscosities are 0.52x10³ pa.s and 0.0133x10-³ pa.s.PROBIEM 1 AssoHE A BONDARY LAYER FOR A Fluid OVER A F|AT PIATE CAN BE APPROKIMATED BY WHERE U= CONSTANT is THE FREE STREAM VelociTy AND S. S(x) is THE THICKNESS Of THE BON DARY LAYER. ) WHICH BOUNDARY CONDITIONS ARE SATISFIED AND WHICH ONES ARE NOT ? 2) calculATE S* AND g* 3) WRITE AN EXPRESSION FOR THEe wall STRESS, AS A PUNCTION OF U, S AND . WHERE Y is THE Visaosire OF THe Fluid. INDICATE THE DIRECTION OF THE STRESS. 4) OBTAIN AN EQJATION FOR S«) FROM THE MOMENTUM INTEGRAI EQUATION 5) OBTAIN S«)of the two liquid levels when the arms are open to the atmosphere. (c) Explain why the pressure difference is not constant across the meniscus of the liquid column in a capillary tube, and discuss the general shape of the meniscus. The surface tension and density of water are 7x 10 'Nm and 10'kgm respectively. in [W]
- Air flow at a constant speed (Ug = 10 m/s) is forming a two-dimensional incompressible laminar boundary layer along a flat plate The velocity profile inside the boundary layer is given by: -2²-² a) Determine the shear stress at the wall, at y = 3 mm and y = 10 mm. b) Calculate the boundary layer displacement thickness. c) Calculate the mass flow rate through the boundary layer per unit width.1. A unknown 30°C liquid (S.G. = 0.85) flows into a surface which creates a shear stress of 0.20 N/m2 and velocity gradient of 16.8 s-1. What is the kinematic viscosity of the liquid? Express answer in exponential notation w/ 4 significant digits. 2. A unknown fluid at 20ºC fills the follow portion of a sleeve with a inner diameter of 11.8 cm and has a fixed coaxial cylinder of diameter 11.6 cm which rotates at 120 rpm. The torque generated is 23.40084214 N∙m per meter of rod length. What is the fluid used and its kinematic viscosity?9) A 2 mm-diameter spherical water droplet with surface tension coefficient of 0.074 N/m². The pressure inside the droplet is ----- (a) 37 kPa (b) 80 kPa (c) 74 Pa (d) None of these 10) For Newtonian fluids, the relation between the shear stress and the rate of deformation (du/dy) is------- (a) Non linear (b) linear (c) none of the above 11) In the figure shown, the------- (a) Adhesion > Cohesion (b) Cohesion > Adhesion
- 1- Consider single-phase fluid flow in a 1-D horizontal reservoir.The reservoir is discretized using four blocks in the x-direction. A well located in block 3 produces at a rate of 400STB/D. All grid blocks have Ax-250ft, w-900ft, h-100 ft, and kx-270md. The FVF and the viscosity of the flowing fluid are 1.0 RB/STB and 2cP, respectively. Identify the interior and boundary blocks in this reservoir. Write the flow equation for block 3 and give the physical meaning of each term in the equation.(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 1The following rheological data were collected on a new "Thick 'n Spicy" brand of tomato catsup at 20°C and 90 kPa. rate of shear (s") shear stress (Pa) 10.0 20.4 20.0 21.5 40.0 23.0 60.0 25.0 80.0 26.5 (a) Plot these measured values on graph-paper. Which class of fluid does the catsup belong to?
- LTE I. 1 A:IY Doc Apr 10 2022 04.23.PDF 10 jo 10 Hw a solid a pe. a vertical axis with agulev Pi I a fluid rotatad velucity (), Theopressure vise (P) in a radial direction depends upon w, v, and f. obtain a form uf equationfor P. 92 the Pressare difference oP in a pipe of diameter Dand length (L) due to Viscous flow depend viscosity (h) and density (S) - obtaind évpression tOP? the Velocity U. on I The officengy of from depends Niscesity ) ,angular velocity (w). diameter of retor (D) and the dischargeO - Express the efficiency in terms of dimensionless. density ) . dywamic on Qus A fluid flow situaton depends the velocity (V), the on density several limear dimension , h,h2. pressure drep DE) » gravity (o), Viscosity As Susface tension (@). and bulk mo dulus of elasticity k. Apply dimen sional analysis. to these variables d AAAAThe following rheological data were collected on a new "Thick 'n Spicy" brand of tomato catsup at 20°C and 90 kPa. rate of shear (s') shear stress (Pa) 10.0 20.4 20.0 21.5 40.0 23.0 60.0 25.0 80.0 26.5 (a) Plot these measured values on graph-paper. Which class of fluid does the catsup belong to? (b) Write the appropriate model for describing the rheological behavior of "Thick 'n Spicy" catsup. Specify the numerical value(s) and the units of the associated constant(s). (c) What shear stress is expected when the rate of shear, under vigorous shaking of a bottle of "Thick 'n Spicy", is 150 s?a all| zain IQ K/s واجب 1 لزوجه.png 0 Q1) The plate in Fig. 1-18 rests on top of the thin film of water, which is at a temperature of 25°C. When a small force F is applied to the plate, the velocity profile across the thickness of the fluid can be described as u = (40y - 800y)m/s, where y is in meters. Determine the shear stress acting on the fixed surface and on the bottom of the plate. 0.32 m/s 10 mm Fig. 1-18