An approximation for the boundary-layer shape inis the formulau(y) - U sin0 sys dwhere U is the stream velocity far from the wall and d is theboundary layer thickness, as in Fig.If the fluid ishelium at 20°C and 1 atm, and if U = 10.8 m/s and 8= 3 cm,use the formula to (a) estimate the wall shear stress Tw inPa, and (b) find the position in the boundary layer where tis one-half of Tw.-- y = 6u(y)

Given data: *The stream velocity of the helium fluid is U=10.8 m/s. *The boundary layer thickness of…

Answered: An approximation for the boundary-layer…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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A cylindrical tank shown below has a radius ? and a circular orifice at the bottom of radius ?. At time ? = 0 the liquid level in the tank is ho. (a) Use the Bernoulli equation to determine the relations between the orifice velocity ?o and the free surface velocity ?s (assume the surface velocity is not zero). (b) Use conservation of mass to determine the orifice velocity in terms of the free surface velocity. (c) Use the results in (a) and (b) to derive a differential equation for h(?). Note that ?s = − dh/dt. d) Separate variables and solve the equation for h(?) with the initial condition h(0) = ho (e) Determine how long it will take to empty the tank.
What is the importance of expressing equations describing fluid dynamics in terms of non-dimensional parameters?Give two examples a of non-dimensional parameters used in fluid mechanics explaining their significance.
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For each statement, choose whether the statement is true or false, and discuss your answer briefly. (a) The velocity potential function can be defined for threedimensional flows. (b) The vorticity must be zero in order for the stream function to be defined. (c) The vorticity must be zero in order for the velocity potential function to be defined. (d) The stream function can be defined only for two-dimensional flow fields.
A subtle point, often missed by students of fluid mechanics (and even their professors!), is that an inviscid region of flow is not the same as an irrotational (potential) region of flow. Discuss the differences and similarities between these two approximations. Give an example of each.
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An isothermal long cylinder with square (side of 0.4 m and diagonal of 0.5657 m) cross-section is placed in a flow with a velocity of 1 m/s as shown. The properties of the fluid are: kinematic viscosity is 1.38 x 10-5 m²/s, thermal conductivity is 0.024 W/m.°C, and Prandtl number is 0.73. What is the average Nusselt number for the flow? 1253 a Figure 1: Flow configuration for Problem 6. The dimensions are: a=0.4 m, b=0.5657 m
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A cube of side (a) and mass (M) is initially sitting fully submerged at the bottom of a container filled with a liquid of kinematic viscosity v and density p. The container has a square cross-section of side (a+a/5) and the cube is sitting right at the middle of the container base. (a) A force (F) starts pulling the cube up at a constant velocity (U). Develop an expression for the force in terms of (U, M. a. g, p and v). You may assume that the velocity in the gap between the cube's sides and the container walls is linear. The expression for (F) is to be valid as long as the cube remains submerged. (b) After the cube reaches the water surface, it continues to be pulled up by the same force. Develop a differential equation for the variation with time of the fraction of the cube that is submerged in water.
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