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fluid_mechanics_hw1.pdf
ESC301: Summer 2015: Problem Set 01 - 1
ESC301
Fluid Mechanics
Summer Semester 2015
Problem Set 1
Assigned: May 22nd, 2015
Deadline for submission: June 2nd, 2015
1) (20 points) Show the dimensions (if any) in the MLtT system of the following ratios,
where ρ is density, V is velocity, l is length, is viscosity, g is the acceleration of gravity, is
frequency, p is pressure, and is surface tension:
a. ρVl
μ
b. V
√gl
c. ω2𝑙
V
d. p
ρV2
e. ρVl
σ
ESC301: Summer 2015: Problem Set 01 - 2
2) (20 points) Given the following velocity field:
V̅ = Ax2y2î − Ax3yj ̂
A[=] 1
m3s
A = 0.75 m-3 s-1
a. Find the expression for the streamline in the xy plane.
b. Velocity of particle at (2 m,3 m).
ESC301: Summer 2015: Problem Set 01 - 3
3) (20 points) An unknown fluid, of SG = 0.560 and viscosity = 2.15 x 10-3 lbf s/ft2, flows
steadily down a surface inclined = 33.0˚ below the horizontal in a film of thickness h = 0.200
in. The velocity profile is given by:
u = ρg
μ (hy −
y2
2 ) sinθ
(Coordinate x is along the surface and y is normal to the surface.) Plot the velocity profile.
Determine the magnitude and direction of the shear stress that acts on the surface.
ESC301: Summer 2015: Problem Set 01 - 4
4) (20 points) Determine the angle of the inclined tube shown below if the pressure at A is
1 psi greater than that at B.
ESC301: Summer 2015: Problem Set 01 - 5
5) (20 points) A tank is constructed of a series of cylinders having diameters of 0.30, 0.25,
and 0.15 m as shown below. The tank contains oil, water, and glycerin and a mercury manometer
is attached to the bottom. Calculate the manometer reading, h. The specific weight of SAE 30 Oil
is 8.95 kN/m3.
