MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 6.13
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
air, Pa
g
water, w > o
w o
oil; o , o
oil layer
b
An oil barge has developed a ne cra

Viscous Flows
A.H. Shapiro and A.A. Sonin 6.16
Problem 6.16
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
air, pa
y
g
h(x, t)
x
viscous liquid
A rigid plane surface is inclined at an angle relative to the horizontal

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 7.14
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
A uid of density and viscosity ows through a long pipe of diameter D at the volume ow

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 7.18
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
A researcher is concerned with the mechanics of sh propulsion. To determine how the t

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 4.19
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
from pump
pa
mass
M
ground
clearance: h
bellows
slot width: w
settling chamber
p0
pb

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 7.12
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
Consider an incompressible ow through a series of geometrically similar machines such

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 6.04
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
Consider a steady, fully developed laminar ow in an annulus with inside radius R2 and

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 7.09
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
A strong explosion (like an atomic bomb) causes a spherically symmetric shock wave to

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 7.03
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
A metal ball falls at steady speed in a large tank containing a viscous liquid. The b

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 5.33
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
At t = 0, a circular tank of radius R contains water at rest, with a depth h. Between

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 5.29
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
The sketch shows a lawn sprinkler with two horizontal arms of radial length R, at the

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 5.33
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
At t = 0, a circular tank of radius R contains water at rest, with a depth h. Between

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 5.32
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
b
V0
v
r
R
The steady sink ow in the sketch is set up by injecting water tangentially

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 5.32
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
b
V0
v
r
R
The steady sink ow in the sketch is set up by injecting water tangentially

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 2.02
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
y
g
h
ys (x)
x
A liquid of density and surface tension has been spilled on a horizont

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 2.07
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
F
air
air
plate
plate
h
liquid
R
A drop of liquid of volume V is squeezed between two

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 6.04a
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
Consider a steady, fully developed laminar ow in an annulus with inside radius R2 an

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 5.02
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
A pipe of area A1 carries a gas at density and velocity V1 . A converging nozzle is m

1.63J/2.26J Advanced Fluid Dynamics
Spring 2014
Problem Set No. 2
Out: Monday, February 24, 2014
Due: Monday, March 10, 2014 (in class, or before 5:00pm in Room 3-362)
Recitation: 4:005:00pm, Wednesday, March 5, 2014 in Room 1-150
Problem 1
It is a common

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 10.3
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
Consider the three dierent, steady, two dimensional incompressible ow elds illustrate

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 9.04
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
U
Porous plate
Suction
Consider a at porous surface with no lengthwise pressure gradi

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 2.06
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
The water strider, or pond skater, is a slender insect, about 1 cm long, that runs or

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 9.09
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
Consider the two-dimensional, incompressible, steady ow of a uid of constant viscosit

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 6.21
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
The sketch shows a circular bearing pad which rests on a at base through the intermed

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 9.03
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
Consider a laminar boundary layer or the laminar sublayer of a turbulent boundary in

2.25
Corrected Solution
Shapiro 6.16
air, pa
y
g
h(x, t)
x
viscous liquid
A rigid plane surface is inclined at an angle relative to the horizontal and wetted by a
thin layer of highly viscous liquid which begins to ow down the incline.
1. Show that if the

MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 6.01
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
Oil is conned in a 10 [cm] diameter cylinder by a piston with a clearance of 0.0002 [

2.25 Fluid Mechanics Fall 2013
Solutions to quiz 1, problem 1
Part a (verbal interpretation of Bernoullis equation)
Along a streamline: Bernoullis equation is essentially a special case of the balance of
energy for a moving fluid element. For steady, in