PROBLEM 1 A two-dimensional velocity field is given by: V = (x - 2y) i- (2r +y) ja. Show that the flow is incompressible and irrotational.b. Derive the expression for the velocity potential, 0(x,y).c. Derive the expression for the stream function, Y(x,y).PROBLEM 2 A smooth, flat plate, 3.0 meters wide and 0.6 meters longparallel to the flow, is immersed in 150C water (p = 999.1 kg/m3 , v = 1.139x 10 6 m 2 /s) flowing at an undisturbed velocity of 0.9 m/s.a) How thick is the boundary layer at the plate's center?b) Find the location and magnitude of the minimum surface shear stressexperienced by the plate.c) Find the total friction drag on one side of the plate

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PROBLEM 1 A two-dimensional velocity field is given by: V = (x - 2y)i- (2x + y)i a. Show that the flow is incompressible and irrotational. b. Derive the expression for the velocity potential, ¤(x,y). c. Derive the expression for the stream function, 4(x,y).

PROBLEM 1 A two-dimensional velocity field is given by: V = (x - 2y)i- (2x + y)i a. Show that the flow is incompressible and irrotational. b. Derive the expression for the velocity potential, ¤(x,y). c. Derive the expression for the stream function, 4(x,y).

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.56P

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Concept explainers

Ising model of Ferromagnets

The Ising model is one of the easiest and most famous theoretical models for ferromagnetism in statistical mechanics. When a group of atomic spins aligns such that their magnetic moments are pointed in the same direction and produce a strong permanent magnetic moment in macroscopic size, the phenomenon is called ferromagnetism. The relative permeability of these magnets is greater than unity and increasing magnetization with the applied external field. Even in the absence of an external magnetic field, these substances retain spontaneous magnetization. An example of ferromagnets is iron.

Question

PROBLEM 1 A two-dimensional velocity field is given by: V = (x - 2y) i- (2r +
y) j
a. Show that the flow is incompressible and irrotational.
b. Derive the expression for the velocity potential, 0(x,y).
c. Derive the expression for the stream function, Y(x,y).
PROBLEM 2 A smooth, flat plate, 3.0 meters wide and 0.6 meters long
parallel to the flow, is immersed in 150C water (p = 999.1 kg/m3 , v = 1.139
x 10 6 m 2 /s) flowing at an undisturbed velocity of 0.9 m/s.
a) How thick is the boundary layer at the plate's center?
b) Find the location and magnitude of the minimum surface shear stress
experienced by the plate.
c) Find the total friction drag on one side of the plate

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