Problem 3. Numerical results for the Blasius solution ✓ for laminar boundary layer flow can be obtained using a Matlab program on my ME 347 Canvas page. (a) Derive the equation for the dimensionless y-component of velocity, v/U, as a function of the similarity parameter (or dimensionless location), n = y√√U/(vx), the dimensionless stream function, f(n) = 4/√Uv x, and the Reynolds number, Re = Ux/v. (b) From the Blasius solution results, calculate the Reynolds number that corresponds to a boundary layer thickness of 8 = 5.0 mm at x = 0.50 m. (c) Plot v/U (on the x-axis) versus y/d = n/5.0 by editing the Matlab code above to include the needed calculations (a tutorial that describes the code above and indicates how to edit the code is available here). Add to your plot the polynomial profile from Homework 2, Problem 1 which is an approximate fit to the Blasius solution. NOTE: Be careful to differentiate between lowercase for the y-component of velocity and the Greek letter v = μ/p (called "nu") for the kinematic viscosity.

Problem 3. Numerical results for the Blasius solution ✓ for laminar boundary layer flow can be obtained using a Matlab program on my ME 347 Canvas page. (a) Derive the equation for the dimensionless y-component of velocity, v/U, as a function of the similarity parameter (or dimensionless location), n = y√√U/(vx), the dimensionless stream function, f(n) = 4/√Uv x, and the Reynolds number, Re = Ux/v. (b) From the Blasius solution results, calculate the Reynolds number that corresponds to a boundary layer thickness of 8 = 5.0 mm at x = 0.50 m. (c) Plot v/U (on the x-axis) versus y/d = n/5.0 by editing the Matlab code above to include the needed calculations (a tutorial that describes the code above and indicates how to edit the code is available here). Add to your plot the polynomial profile from Homework 2, Problem 1 which is an approximate fit to the Blasius solution. NOTE: Be careful to differentiate between lowercase for the y-component of velocity and the Greek letter v = μ/p (called "nu") for the kinematic viscosity.

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 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...

See similar textbooks

Similar questions

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?
(a) In a variety of environmental problems, it is common to find fluid motions that have a cellular character; i.e. the fluid streamlines form closed loops in the form of a cell. An example of a 2D cellular flow is ū = sin(rx) cos(ry)î – cos(rx) sin(ry)j (i) Is this flow incompressible? (Justify you answer.) (ii) Calculate the vorticity. (iii) Where is the magnitude of the vorticity highest, and where does it vanish?
A proposed harmonic function F(x, y, z) is given byF = 2x2 + y3 - 4xz +f(y)(a) If possible, fi nd a function f (y) for which the laplacianof F is zero. If you do indeed solve part (a), can your fi nalfunction F serve as (b) a velocity potential or (c) a streamfunction?
A 1:7 scale model simulates the operation of alarge turbine that is to generate 200 kW with a flowrate of 1.5 m3/s.What flow rate should be used inthe model, and what power output is expected?(a) Water at the same temperature is used in bothmodel and prototype.(b) The model water is at 25°C and the prototypewater is at 10°C.
A periodic Kármán vortex street is formed when an uniform stream flows over a circular cylinder (Figure Q4). By applying method of repeating variables or Buckingham Pi's Theorem, determine a dimensionless relationship for Kármán vortex shedding frequency (fx.) as a function of free-stream speed (V), fluid density (p), fluid viscosity(u), and cylinder diameter (D). Q4 V D Figure Q4
Problem 01 t* = 0.015s 100 m In 1940, fluid dynamicist G. I. Taylor determined from Dimensional Analysis that the radius R of a fireball created by a nuclear explosion is exclusively determined by the released energy E, initial gas density po and elapsed time t* since detonation. Note: 1 kiloton = 4 × 1012 J (Joules). (a) List in a table the primary dimensions of R, E, po and t*. How many primary dimensions are there? (b) Find the single Pi group that controls the blast radius R. (c) In 1945, an experiment was conducted in the desert of New Mexico with a 20 kiloton bomb. On that day, air density was recorded at po = 1.23kg/m³. The photograph above taken at t* 0.015s shows a radius R108 m. Compute the value of the Pi group you have found. (d) Assuming that the Pi group remains constant, find the blast radius R at t* = 0.02s.
[1] Consider steady flow of air through the diffuser portion of a wind tunnel. Along the centerline of the diffuser, the air speed decreases from uentrance to ut as sketched. Measurements reveal that the centerline air speed decreases parabolically through the diffuser. Write an equation for centerline speed u(x), based on the parameters given here, Dee x=0 to x=L.
Find the equation of motion (Navier Stokes) for a viscous fluid between two rotating concentric cylinders (axle and shaft). The inner cylinder has the radius ro and rotates at angular speed wo. The outer cylinder has the radius R and is stationary. Write down each vector component of the equation in a separate line and use reasonable assumptions to simplify the equation, especially the derivatives. Be sure to use cylindrical coordinates for the convective operator and the other derivatives.
The slope of the height h of a surface wave moving in a shallow pool of liquid is related to the speed of the wave u and gravity g by the following equation и ди дх g əx (a) Use a length scale L and a velocity scale Vo to 'nondimensionalize' the equation (b) What is the nondimensional parameter of the flow?
Plz help me to get solution of this fluid mechanics question. File is attached
Find the vorticity of the fluid motion for the given velocity com- ponents. KINEMATICS OF FLUIDS (a) u A(x + y), v = - A(x + y) (b) u = 2Axz, (c) u Ay²+ By + C, v = A(c² + x² - z²) 1)=0
The time t d to drain a liquid from a hole in the bottom of atank is a function of the hole diameter d , the initial fluidvolume y 0 , the initial liquid depth h 0 , and the density ρ andviscosity μ of the fluid. Rewrite this relation as a dimensionlessfunction, using Ipsen’s method.