Consider irrotational flow past a stationary sphere of radius R located at the origin. In the limit r→ ∞, the velocity field v = = U2, as in Fig. 8-6 in the book. (a) Calculate the velocity field v assuming potential flow given by v = Vo(r, 0, 0), where the potential can be assumed to be independent of the azimuthal coordinate and v=0. Here, since Ә rde ə V₁ = - U cos and ve Ər for large r/R, look for solutions of the form = f(r) cos 0. Assume a no-penetration boundary condition at the surface of the sphere. (b) Calculate the pressure P and the drag force due to pressure. -U sin 0

Consider irrotational flow past a stationary sphere of radius R located at the origin. In the limit r→ ∞, the velocity field v = = U2, as in Fig. 8-6 in the book. (a) Calculate the velocity field v assuming potential flow given by v = Vo(r, 0, 0), where the potential can be assumed to be independent of the azimuthal coordinate and v=0. Here, since Ә rde ə V₁ = - U cos and ve Ər for large r/R, look for solutions of the form = f(r) cos 0. Assume a no-penetration boundary condition at the surface of the sphere. (b) Calculate the pressure P and the drag force due to pressure. -U sin 0

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: 10 Fig. (6) 8 MPa

A: Given Dataσx=8MPaθ=24°

Q: A simple approximate velocity field for this flow of the Converging duct flow is modeled by the…

Q: 4. A steady, incompressible, and two-dimensional velocity field is given by the following components…

A: The step by step solution is provided below.

Q: In a certain two‐dimensional flow field, the velocity is constant with components u = –4 ft/s and v…

A: to find:the velocity potential function for the flow fieldthe stream function for the flow…

Q: A two-dimensional incompressible velocity fi eld has u =K (1 - e - ay ), for x ≤ L and 0 ≤ y ≤ ∞.…

A: Write the expression for the continuity equation.

Q: A two-dimensional flow field is given by u = 5x 2 − 5y 2v = −10xy (i) Find the streamfunction ψ and…

Q: A steady, three-dimensional velocity field is given by V = (0.657 +1.73x +0.948y+as) + (2.61 +cr…

Q: Calculate the material acceleration for the following steady, incompressible velocity field:

A: Given: Velocity fieldV→=0.5+0.8xi^+1.5-0.8yj^

Q: For the flow field described by u = 2, v = yz2t, w = −z3t/3. (a) Is this flow one-, two-, or…

A: Since you have asked question with multiple parts we will answer first two parts for you. Part…

Q: Although many pots and pans are made of stainless steel, the bottoms often have either a roll-bonded…

A: The material properties are as follows. Material Thermal conductivity Specific Heat Thermal…

Q: Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and…

A: Given that :Flow is two dimensional flowVelocity field terms are given u=1v=2ytAsking to calculate…

Q: The stream function of a flow field is ų = Ax3 – Bxy², where A = 1 m-1s1 and B = 3 m1s1. (a) Derive…

A: The velocity along the x axis can be determined as shown below.

Q: Question 2. In a particular fluid flow, the Eulerian velocity is given by u= (- x², 3xy, (3y -…

A: Given:The Eulerian velocity is .The density field is and .Formula used:The flow is incompressible…

Q: Question 3 : A line source at y-axis is located 1 m above the horizontal plate (x-axis), where the…

A: The objective of the question is to determine the stream function of the potential flow in both…

Q: 1. For incompressible flows, their velocity field 2. In the case of axisymmetric 2D incompressible…

Q: velocity field is given by: A two-dimensional V = (x - 2y) ï- (2x + y) j a. Show that the flow is…

A: V= (x-2y) i^- (2x+y) j^

Q: or the velocity field: u = 3xy, v = -1.5y²+5; for water, ρ = 1000 kg/m³ If the pressure at (0,0) is…

A: The velocity field is .The density of water is .The pressure at is .

Q: Consider 3D flow with velocity components below. u=x²+2xy v=2x-y²+z² W=-2xz+y² a. Is this flow…

A: Given data:- 3D flow with velocity components below.U=x2+2xyV=2x-y2+z2W=-2xz+y2To check:- flow…

Q: "A steady, incompressible, two-dimensional velocity field is given by V = (u, v) = (2.7-1.75x, 0.7+…

Q: Two velocity components of a steady, incompressible flow field are given as follows; u = 2ax + bxy +…

Q: Is of a uniform flow filed, a d-

A: False

Q: Given velocity fieldV(x,y,z,t) = (5xy² + t)i + (2z + 8)j +18km/s, with x,y,z in meters and it in…

Q: 2. Find the rate of deformation for a line vortex with velocity field V=YG x² + y² Ans. E = -8 39…

Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

Consider irrotational flow past a stationary sphere of radius R located at the
origin. In the limit r→∞, the velocity field v = U2, as in Fig. 8-6 in the
book.
(a) Calculate the velocity field v assuming potential flow given by v =
Vo(r, 0, 0), where the potential can be assumed to be independent
of the azimuthal coordinate and vo= 0. Here, since
ə
rde
Ə
Ər
for large r/R, look for solutions of the form = f(r) cos 0. Assume a
no-penetration boundary condition at the surface of the sphere.
(b) Calculate the pressure P and the drag force due to pressure.
Vr =
U cos 0 and Vo =
-U sin 0

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Write the given data and what is to find

VIEW

Step 2: Determine the general solution for the laplace equation:

VIEW

Step 3: Determine the values of the coefficients A and B:

VIEW

Step 4: Determine the velocity distribution expression:

VIEW

Step 5: Determine the velocity distribution profile in r and theta directions:

VIEW

Step 6: Determine the pressure at the surface:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 7 steps with 59 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Fluid mechanics
4. Consider the steady, two-dimensional velocity field given by: u = 2xy-y²; v=x-y². Show that it is a possible 2d incompressible flow. Find the component of acceleration in x direction of a fluid particle at point (x, y) = (1,2)
Question 3 Consider the two-dimensional incompressible velocity potential O = xy + x² – y2 a) Show that this flow is irrotational. b) Find the stream function Y(x, y), if Y(0,0) = 0 .
For the velocity field in u = Ax , υ = By , and w = Cxy , the convectiveacceleration in the x-direction is( a ) Ax 2 , ( b ) A 2 x , ( c ) B 2 y , ( d ) By 2 , ( e ) Cx 2 y
3.14. Find the vorticity in polar coordinates for the following velocity com- ponents (a) v=rsin 0, ve = 2r cos 0 (b) v = cos 0, 11=0
The stream function o in a two-dimensional flow field is given as 9 = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. Find the potential flow function P(x, y) for this flow field with boundary condition 0 = 0 at x = 2, y = 1. (b)
c. For a given velocity field calculate the constants a, b, and c such that the flow field is irrotational. V = (0.657 + 1.73x + 0.948y + az)i + (2.61 + cx + 1.91y + bz)j+(-2.73x - 3.66y – 3.64z)k
Homework What is the third velocity component such that continuity equation is satisfied if two components are u = 1. 2y2, w = 2хyz ? 2. Consider the following steady, two-dimensional, incompressible velocity field V = (Ax? + B)i + (-Ay + Cx²)j where A, B, and C are constants. Calculate the pressure as a function of x and y.