(a) Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

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Answer 1

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Chapter 4, Problem 67P

To determine

(a)

Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

To determine

(b)

Whether the flow is compressible or not show them by calculating the linear strain rate of the fluid particle at both times.

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An incompressible fluid of density ρ and viscosity μ flows down a plane inclined at an angle α.Assume constant gravitational acceleration downward, fully-developed flow, constant pressure inthe air outside the fluid, and zero stress exerted by the air on the fluid. i) Starting from the incompressible Navier-Stokes equations, derive the differential equation andboundary conditions that govern the velocity u(y). ii) Solve the equation from the previous part for u(y). iii) Using your solution, calculate the following quantities: The mass flow rate (per unit depth) down the channel. The vorticity vector, ~ξ, and rate-of-strain tensor, epsilon at a point (x, y) in the channel. The shear stress exerted by the fluid on the bottom wall The viscous force in the fluid iv) Consider a control volume consisting of a section of length L of the channel. Demonstratethat the conservation of x momentum holds for this control volume by integrating appropriatequantities over its perimeter and…

Engine oil at 60°C rotates as a rigid body about the z-axis in a spinning cylindrical container. There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface (zsurface as a function of r). (Hint: P = Patm everywhere on the free surface. The flow is rotationally symmetric about the z-axis.)

Answer 2

Question

Chapter 4, Problem 67P

To determine

(a)

Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

To determine

(b)

Whether the flow is compressible or not show them by calculating the linear strain rate of the fluid particle at both times.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Chapter 4, Problem 67P

To determine

(a)

Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

To determine

(b)

Whether the flow is compressible or not show them by calculating the linear strain rate of the fluid particle at both times.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 4, Problem 67P

To determine

(a)

Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

To determine

(b)

Whether the flow is compressible or not show them by calculating the linear strain rate of the fluid particle at both times.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 4, Problem 67P

To determine

(a)

Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

To determine

(b)

Whether the flow is compressible or not show them by calculating the linear strain rate of the fluid particle at both times.

Answer 6

Chapter 4, Problem 67P

To determine

(a)

Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

Answer 7

Chapter 4, Problem 67P

To determine

(a)

Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

Answer 8

To determine

(b)

Whether the flow is compressible or not show them by calculating the linear strain rate of the fluid particle at both times.

Answer 9

To determine

(b)

Whether the flow is compressible or not show them by calculating the linear strain rate of the fluid particle at both times.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

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(a) Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

Solution Summary: The author explains the flow is incompressible by calculating the volume of the fluid particle at both times.

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(a)

Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

(b)

Whether the flow is compressible or not show them by calculating the linear strain rate of the fluid particle at both times.

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Chapter 4 Solutions

(a) Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

Solution Summary: The author explains the flow is incompressible by calculating the volume of the fluid particle at both times.

Videos

(a) Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

(b) Whether the flow is compressible or not show them by calculating the linear strain rate of the fluid particle at both times.

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Chapter 4 Solutions

(a)

Whether the flow is compressible or not show them by calculating the volume of the fluid particle at both times.

(b)

Whether the flow is compressible or not show them by calculating the linear strain rate of the fluid particle at both times.