Connect with LearnSmart for Anderson: Fundamentals of Aerodynamics, 6e
6th Edition
ISBN: 9781259683268
Author: Anderson, John
Publisher: Mcgraw-hill Higher Education (us)
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Chapter 10, Problem 10.18P
Consider a centered expansion wave where
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Example 10.4-1 Stream Functions for a Flow Field
The velocity components for a flow field are as follows:
v, = a(x² – y²³), v, =-2axy
V.
V.
%3D
Prove that it satisfies continuity equation for two dimensional flows and find y. Plot streamlines
for y=1 to y=6.
The stream function relation is given as:
Y = xy
Find the equations for the components of velocity. Check if we satisfy continuity. Also, plot
streamlines for a constant y=4 and y=1.
Simulation of laminar gas flow in the pipe with Ansys Fluent
Task:
1. Calculate velocity distribution in y axis at inlet and outlet of the pipe. Submit it as a chart.
2. Calculate velocity distribution over the pipe length. Submit it as a chart.
Figure. pipe geometry
L, m = 16
R, m= 0.15
Inlet velocity, m/s= 0.08
Gas= Oxygen
Need proper solution like pdf file, don't need steps by steps. If you can can do it through ansys fluent. Write proper solution on word file or pdf.
Chapter 10 Solutions
Connect with LearnSmart for Anderson: Fundamentals of Aerodynamics, 6e
Ch. 10 - The reservoir pressure and temperature for a...Ch. 10 - A flow is isentropically expanded to supersonic...Ch. 10 - A Pitot tube inserted at the exit of a supersonic...Ch. 10 - For the nozzle flow given in Problem 10.1, the...Ch. 10 - A closed-form expression for the mass flow through...Ch. 10 - Prob. 10.6PCh. 10 - A convergent-divergent nozzle with an...Ch. 10 - For the flow in Problem 10.7, calculate the mass...Ch. 10 - Consider a convergent-divergent nozzle with an...Ch. 10 - A 20 half-angle wedge is mounted at 0 angle of...
Ch. 10 - The nozzle of a supersonic wind tunnel has an...Ch. 10 - We wish to design a supersonic wind tunnel that...Ch. 10 - Consider a rocket engine burning hydrogen and...Ch. 10 - For supersonic and hypersonic wind tunnels, a...Ch. 10 - Return to Problem 9.18. where the average Mach...Ch. 10 - Return to Problem 9.19, where the average Mach...Ch. 10 - A horizontal flow initially at Mach I flows over a...Ch. 10 - Consider a centered expansion wave where M1=1.0...
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- Question 3 : A line source at y-axis is located 1 m above the horizontal plate (x-axis), where the flow rate per unit length is, m²/s.. (a) Using x, and, y, in m, write the stream function of the potential flow in both Cartesian and polar coordinates. (b) Express the radial component velocity in polar coordinates and hence find the velocity magnitude at, x = 0, and, y = 2. (c) Calculate the radial and angular component velocity at, x = 1, and, y 1, and hence find the velocity magnitude and direction. (d) If the source is placed near a corner where the distance from horizontal and vertical plate are 1 m, determine the stream function of the potential flow and find the velocity on the horizontal plate right below the source. =arrow_forward1) The velocity profile of a viscus fluid over a plate is parabolie with vertex 25 em from the plate ,where the velocity 125 cm/s. calculate the velocity gradient and shear stress at distance of (0, 5, 15 and 25 cm) from the plate given the viscosity of the fluid =7 poise ? Also draw the figure explain the relationship between the velocity gradient and shear stress. Take velocity profile for parabolic equation, (v = ay + by + c)arrow_forwardQuestion 4: The velocity field of a flow is given by V = axyi + by'j where a = 1 m's' and b = - 0.5 m's". The coordinates are in meters. Determine whether the flow field is three-, two-, or one-dimensional. Find the equations of the streamlines and sketch several streamlines in the upper half plane (2.arrow_forward
- Problem 1 Given a steady flow, where the velocity is described by: u = 3 cos(x) + 2ry v = 3 sin(y) + 2?y !! !! a) Find the stream function if it exists. b) Find the potential function if it exists. c) For a square with opposite diagonal corners at (0,0) and (47, 27), evaluate the circu- lation I = - f V.ds where c is a closed path around the square. d) Calculate the substantial derivative of velocity at the center of the same box.arrow_forwardProblem 2: Obtaining velocity components from streamlines The stream function for a particular flow is given by the equation: y = 2x² - 2y? Determine the velocity components of the flow, make sure we satisfy continuity and plot the %3D2x² streamlines.arrow_forwardExample 10.4-2 Stream Function and Velocities from potential Function The potential function for 2D, irrotational, incompressible flow filed is given as: Ø = x² – 2y – y² %3D Find the stream function y and the velocity components and y?arrow_forward
- Given the vector equation below for velocity of a given fluid: V=(0.5+1.2x)i + (-2.0-1.2y)j, derive an analytical expression for the flow streamlinesarrow_forwardCX a) Investigate whether the function o represents the velocity potential x²+y2 of a particular incompressible 2D flow, and if so, what should be the dimension of constant C which has value of 2.arrow_forwardA flow is described by the flow field of vec(V)=A(1+Bt)hat(i)+Ctyhat(j), where A=1 m/s, B=1 s -1 , and C=1 s -2 . The unit for the coordinates is meters. a. Plot the pathline that passes through the point (x=1 m, y=1 m) at time t=0 . b. Compare the streamlines through the point (x=1 m, y=1 m) at time t=0, 1, and 2 s. c. Calculate the acceleration at time t=0 along the streamline passing the point (x=1 m, y=1 m) at time t=0 .arrow_forward
- the black sqaure is delta (change) in pressure Assume that p is a function of average velocity V, pipe length L and diameter D, the pipe roughness e (mean height of roughness of the pipe wall, e.g. in microns), and the fluid density . 1.How many nondimensional parameters are needed to define the nondimensional pressure-drop vs. flow relationship in the pipe? 2. Using (D, , and V) as repeating parameters, derive the nondimensional pressure drop and other required parameters to relate p, V, L, D, e , and .arrow_forwardProblem 3: Obtaining the stream function from velocity components The steady state, incompressible flow field for two-dimensional flow is given by th velocity components: v = 16 y - x and v = 16x+y %3D %3D Determine the equation for the stream function and make sure continuity is satisfiearrow_forwardConsider the flow field V = (ay+dx)i + (bx-dy)j + ck, where a(t), b(t), c(t), and d(t) are time dependent coefficients. Prove the density is constant following a fluid particle, then find the pressure gradient vector gradP, Γ for a circular contour of radius R in the x-y plane (centered on the origin) using a contour integral, and Γ by evaluating the Stokes theorem surface integral on the hemisphere of radius R above the x-y plane bounded by the contour.arrow_forward
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