fa khara ny
PHAROS UNIVERSITY
FACULTY OF ENGINEERING
MECHANICAL ENGINEERING Dept.
Date :
14 Oct. 2012
Fall 2012/2013.
Level
Semester 1
Code ME 253 Title: Fluid MechanicsII
Home work # 3 Navier – Stokes & Euler Equations
Problems for N-S & Euler Equations
httpwww.pua.edu.egPage.aspxPage=Faculties-%3eEngineering-%3eFall+Semester
Question # 1
A liquid flows down an inclined plane surface in a steady, fully developed
laminar film of thickness h. Simplify the continuity and Navier-Stokes
equations to model this flow field. Obtain the velocity profile, the shear
stress distribution, the volume flow rate and average velocity. Calculate the
volume flow rate in a film of water h=1 mm thick, flowing on a surface b=1
m wide, inclined at ϴ =15o to the horizontal (see Figure of Q #5)
Question # 2
Given u = Umax ( 1- (y/h)2 ) & Umax = -(dp/dx) h2/2μ at y=0 for flow
between fixed parallel plates Find:
1-Wall shear stress 2-Stream function 3-Vorticity 4-velocity potential
5- average velocity
Question # 3
Avelocity field is proposed to be:
u=10y/(x2+y2) & v = - 10x/(x2+y2) & w=0
is this a possible incompressible flow ? .If so Find the pressure gradient
▽P, assuming a frictionless air flow with the z-axis vertical.(ϱair =1.23 kg/m3)
Question # 4
A constant-thickness film of viscous liquid flows in laminar
motion down a plate inclined at angle ϴ. The velocity profile is
u = Cy(2h - y) & v = w= 0
Find the constant C in terms of the specific weight and viscosity
and the angleϴ. Find the volume flux Q per unit width
in terms of these parameters.
Dr. Alaa Shibl
Eng.
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