Consider the flow with velocity field given as1(F·X)xF8TTurur2with Ha given constant, F a given constant vector and r=Vx +y? + z?.Do fluid particles rotate?Do they change volume?What is the rate of change of the angle between two initially orthogonal line elements?

Given : To find : Do fluid particles rotate

Consider the flow with velocity field given as (F·x)x 1 F- 8TTur u ( with Ha given constant, F a given constant vector and r =/x +y +y?+z?. Do fluid particles rotate? Do they change volume? What is the rate of change of the angle between two initially orthogonal line elements?

Consider the flow with velocity field given as (F·x)x 1 F- 8TTur u ( with Ha given constant, F a given constant vector and r =/x +y +y?+z?. Do fluid particles rotate? Do they change volume? What is the rate of change of the angle between two initially orthogonal line elements?

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: A particle moves along a straight line such that its acceleration is a = (8t^2 - 5) m/s^2, where ( s…

Q: *. 25 Block & has a controlled position in the slot given by y- V120 sin(at/10) in. for 0sts 10 sec.…

Q: The sides of a thin rectangular block are measured using different digital calipers as 25.00 + 0.05…

A: In case of sum of subtraction, uncertainties are simply added.

Q: Does torque increase with slip? What happens to torque when slip was 0.02 then becomes 0.03?

A: Concept: 1) In between two components, to transfer torque from one to another, there should not be…

Q: The change in bending moment for a beam between points A and B is equal to the Select the correct…

Q: piston–cylinder assembly contains a two-phase liquid–vapor mixture of H2O at 200 lbf/in.2 with a…

Q: At the instant shown the 100-lb block A is moving down the plane at 8 ft/s while being attached to…

A: Weight of the block A, WA= 100 lb Weight of the block B, WB= 50 lb Velocity, u= 8 ft/s Coefficient…

Q: A mass weighting 24 lbs stretches a spring 3 inches. The mass is in a medium that exerts a viscous…

Q: You are designing a rod with a fixed geometry with al inch diameter and a 20 inch length. The…

A: Given that, In existing design, Material used for rod is 2014 T6 Aluminum. Since after analysis,…

Q: For a point under a plane state of stress, the stresses on the vertical and horizontal planes are…

A: Find the normal stress at inclined surface. And location of principal plane.

Q: A cantilever beam of span l carries a uniform distributed load of intensity w throughout its span.…

A: GIVEN DATA- A UDL CANTILEVER BEAM GIVEN WE HAVE TO FIND MAXIMUM BENDING MOMENT

Q: A force F of 40000 lbf is applied to rod AC the negative Y-direction. The rod is 1000 inches tall. A…

A: Given: The force, F = 40000 lbf The force, R = 75 lbf The force, P = 25 lbf The fillet radii, r =…

Q: Determine the axial load at point B for the beam below. 12 k 60° B 8k Lsntsnsnsn -5 ft- Select the…

A: GIVEN DATA- A CANTILEVER BEAM GIVEN LOADED WITH POINT LOAD WE HAVE TO FIND AXIAL FORCE AT B

Q: 24 kN/m D. C. Hinge m 5 m 2 m- 3m- FIG. P4.39

A: Given: Uniform distributed load→w=24 KN/m Let upward reactions at point A, B, D are→RA, RB, RD…

Q: The only instrument among the followings that is normally not connected to the aircraft electrical…

A: In the aircraft, there are many instruments that are used to check the condition of the various…

Q: Calculate the polar radius of gyration of the shaded area about the center O of the larger circle.…

Q: 6-5. A particle of mass m is embedded at a distance / from the center O of a massless circular disk…

Q: A pulley 24 inches in diameter transmits 53 and a half horsepower at 500 rpm. The arc of contact…

A: Given, Diameter of the pulley = d = 24 in Power transmitted by pulley = P = 53.5 hp = 53.5 x 550…

Q: F3-5. If the mass of cylinder C is 40 kg. determine the mass of cylinder A in order to hold the…

A: Find the mass of cylinder A.

Q: A rectangular duct whose cross-section has a w of 3 m and a h of 1.5m is used to transfer cooled…

A: Given:b=3 mh=1.5 m

Q: The ratio of stress to bulk modulus for compression of the material. Select the correct response.…

A: Ahjaa

Q: Both portions of the rod ABC are made of an aluminum for which E = 70.4GPa. Knowing that the…

Q: Determine the total surface area and volume of the solid generated by revolving the area shown…

Q: Determine the moment of inertia about the x-axis of the rectangular area without and with the…

A: GIVEN DATA- A RECTANGLE CROSS SECTION GIVEN WE HAVE TO FIND MOI ABOUT X-AXIS

Q: Water at 65 degrees Celsius is flowing horizontally at a rate of 84.1 m^3/hr in a pipe. It enters a…

Q: A light aircraft is flying at an altitude of 1000 m. If the wing chord is 1.5 m, and the freestream…

A: Given: Altitude of the aircraft→h=1000 m At this altitude: Density of the air→ρ=1.11 Kg/m3 And…

Q: generator has a combined steam rate of 5.35 kg/kwh at its rated output of 20,000 kw. The steam is at…

Q: A gas-turbine power plant operating on an ideal Brayton cycle has a pressure ratio of 8. The gas…

Q: Water in a hydraulic press, initially at 139 kPa absoute, is subjected to a pressure of 116202 kPa…

A: Find the percentage decrease in volume.

Q: 30 kN 140 kN m 2 m- 3m -2 m

Q: If 8.5kg of of air are compressed isothermally from 90kPa 8m3 to 600kPa. Find the Work for a nonflow…

A: Given: P1 = 90 kPa P2 = 600 kPa V1 = 8 m3

Q: A continuous gravity decanter is used to separate two immiscible liquids, oil (SG = 0.76) and water.…

A: Given information A continuous gravity decanter is used to separate two immiscible liquids. oil (SG…

Q: 1. 1) The acceleration of a particle moving along a straight line is (-C· /v) m/s², where Cis a…

A: Given, Acceleration of a particle as a function of velocity = a = - C v C = 1.5 Initial velocity =…

Q: * Drow a (Staress Strain), Diagram of a materñal High Brittleness specifyng the with Yield stress…

A: Stress -Strain Curve of Brittle material

Q: Q2 (a) List several types of flexible drive system and its application in real engineering.

A: Different types of flexible drive system and it's application

Q: A 40 MW steam plant working on the Rankine cycle operates between boiler pressure of 4 MPa and…

A: Answer: (a) The cycle efficiency is 30%. (b) The quality of steam from the turbine exit is 0.88343.…

Q: The system in the figure is in equilibrium. A concrete block of mass 164 kg hangs from the end of…

Q: Determine the following based on the given: a) velocity of point A (in/s), b) the angle of Va with…

Q: (QA2) Air is fed to a perfectly insulated turbine at 6 bar and exits the turbine at 1 bar and 300 K.…

Q: Sunflower oil (SG = 0.7, viscosity = 154cP) is pumped at a rate of 85 ft^3/min (ID = 3.5in) from…

A: Specific gravity of Sunflower oil, SG=0.7Viscosity of the Sunflower oil, μ=154 cp…

Q: A Rankine cycle operates with steam under the same conditions as a simple ideal Rankine cycle engine…

Q: : A rod made of carbon reinforced epoxy has a diameter 2.5 cm, length 1.25 m, and mass 0.95 kg. The…

Q: (4) A turbine receives steam at 10 MPa, 600°C and exhaust it at 0.2 MPa. (a) for the ideal Rankine…

Q: 3. In the figure below, the coefficient of sliding friction for all contact surfaces is 0.20. When…

Q: Determine the state of stress at point A on the cross section of the pipe assembly at section a-a.…

Q: Determinant of 2 x 2 Matrices. Solve for the determinant of the following matrices: 1. A = 4 2. B =…

Q: Explain the operation and maintenance considerations for the foot brake assembly from the Harrison…

A: Given Foot Brake To find Operation Maintenance

Q: 5. If 25 x 106 kg/h flows over a waterfall that is 200 m high, what ideal power in kilowatts can be…

Q: Enumerate and name the fittings you can find base on the figure. Use table to organize your answer.…

A: Concept: Fitting are used in plumbing design to takes branches or loops for joining different…

Q: Determine the moment at point A for the beam shown. 10 k 45° 50k-ft -6 ft- -6 ft- Select the correct…

A: Find the moment at point A.

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 the flow with velocity field given as
1
(F·X)x
F
8TTur
u
r2
with Ha given constant, F a given constant vector and r=Vx +
y? + z?.
Do fluid particles rotate?
Do they change volume?
What is the rate of change of the angle between two initially orthogonal line elements?

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 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

An incompressible velocity field is given by u=a(x°y²-y), v unknown, w=bxyz where a and b are constants. (a)What is the form of the velocity component for that the flow conserves mass? (b) Write Navier- Stokes's equation in 2-dimensional space with x-y coordinate system.
Home Work (steady continuity equation at a point for incompressible fluid flow: 1- The x component of velocity in a steady, incompressible flow field in the xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find the simplest y component of velocity for this flow field. 2- The velocity components for an incompressible steady flow field are u= (A x* +z) and v=B (xy + yz). Determine the z component of velocity for steady flow. 3- The x component of velocity for a flow field is given as u = Ax²y2 where A = 0.3 ms and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Assume incompressible steady two dimension flow
4s-1, Given the velocity field V = Axî – Ayĵ, where A %3D (a) Sketch the velocity field. (you can do this by hand or use software of your choice)
1. If u- 3x'yr and v = -6x'y'r answer the following questions giving reasons, Is this flow or fluid: (a) Real (Satisfies Continuity Principle). (b) Steady or unsteady. (c) Uniform or non-uniform. (d) One, two, or three dimensional. (e) Compressible or incompressible. Also, Find the acceleration at point (1,1). %3D
1) A steady, incompressible, two-dimensional velocity field is given by the following components in the xy-plane: V(u, v) = (0.25 +1.4x + 0.8y)i + (-0.5 +0.9x - 1.4y)] where the x- and y-coordinates are in m and the magnitude of velocity is in m/s. a) Calculate the acceleration field (find expressions for acceleration components ax and ay) b) Calculate the acceleration at the point (x, y) = (2, 3).
A velocity field of the two-dimensional, time-dependent fluid flow is given by where t is time. Find the material derivative Du/Dt and hence calculate the acceleration of the fluid at any time t > 0 and any pont x > 0, y > 0. a) Incompressibility a) Is this flow incompressible (i.e. it has zero divergence)? Yes No ди Ət b) Time derivative of flow field Calculate the time derivative of the velocity. Represent your answer in the form i+ || 3 3 u(t, x, y) =r? (x² + y² ) i− {etxtyj X уј 3 a = c) Material derivative and acceleration Calculate the material derivative of the velocity and hence the acceleration a. Represent your answer in the form Du Dt || j i+ j
The velocity potential for non-viscous two-dimensional and uncompressed water flow in Cartesian coordinates is given as D= -(3x²y - y³) a) Find the corresponding current function. b) Find the pressure difference between points (1,2) and (4,4). Omit the height difference
(b) One form of fluid movement is rotation and deform angularly. Figure Q1(b) shows the rotation and angular deformation caused by velocity variation about z-axis. Based on Table 1 and setting given to you, derive an equation of rotation. ди Sy St ây > B' ĉu B B ôy dy A' ↑ Sa v+. ôx A ôx Figure Q1(b) : Rotation and Angular Deformation Table 1: Axis of Rotation Setting Axis of Rotation 2 у-ахis
= [2x² + y³ , flow. Is the flow irrotational? Q4) Let v xyz + 2y, xy + zy] be the velocity vector of steady fluid
Numerical Problem: Round off your final answers into 2 decimals only. a) The velocity vector in a fluid flow is given as V = 1xt- 12x?yj + 3tk. Find the resultant velocity and acceleration of a fluid particle at (1,3,4) at time t=1. b) Determine the third component of velocity such that they satisfy the continuity equation: v = 3y and w = 1ryz?. c) Find the convective acceleration at the middle of a pipe which converges uniformly from 0.2 m diameter to 0.12 m diameter over 2 m length. The rate of flow is 30 liters per second.
1. Stagnation Points A steady incompressible three dimensional velocity field is given by: V = (2 – 3x + x²) î + (y² – 8y + 5)j + (5z² + 20z + 32)k Where the x-, y- and z- coordinates are in [m] and the magnitude of velocity is in [m/s]. a) Determine coordinates of possible stagnation points in the flow. b) Specify a region in the velocity flied containing at least one stagnation point. c) Find the magnitude and direction of the local velocity field at 4- different points that located at equal- distance from your specified stagnation point.
Ay j. Is this a possible case of incompres- 3.9 A velocity field is given by V= Axyi -- %3D sible flow? If yes, obtain the stream function and find the value of constant A for which the flow rate between the streamlines passing through the points (3, 3) and (3, 4) is 18 units. Axy Ans: V = 12 + C, A 7 2