CHAPTER 17: Temperature, Thermal Expansion, and the Ideal Gas Law
Responses to Questions
2.
Properties of materials that could be exploited in making a thermometer include:
a.
thermal expansion, both linear and volume
b.
the proportionality between temper
PHYSICS 4B
FINAL EXAM
SPRING QUARTER 2013
PROF. HIRSCH
8 Problems
JUNE 11th
Please write in pen rather than in pencil. No regrading for finals written in pencil.
Write clearly and justify all steps.
Problem 1 (10 pts+2 pts extra credit)
10cm
10cm
5cm
?
20
Question
Viscous liquid of constant density and constant kinematic viscosity is at
rest in the region o y h between two rigid parallel plates. There are
no body forces. At time t = 0 the top plate is set into motion parallel to
its own plane with speed U
Question
(i) Using tensorial notation, or otherwise, prove the vector identities
.(a) = .a + (a.)
( a) = 2 a + (.a)
a ( a) = (a2 /2) (a.)a
for a general suitably differentiable scalar function and vector a.
(ii) Explain briefly the major differences betw
Question
Steady viscous incompessible flow takes place parallel to the z-axis in a cylindrical pip of cross section D. The kinematic viscosity and density of the fluid
are both constant and are given by and respectively and there are no
body forces. By as
H.P. Paar
PHYS 4B: Mechanics, Fluids, Waves & Heat
Spring 2015
Quizz # 3 solutions
Solutions by Yury Kiselev
1. (15 points)
(a) (5 points) Distance from the station L = vT tt = vL tL .
The problem could be understood dierently that we are not given times
H.P. Paar
PHYS 4B: Mechanics, Fluids, Waves & Heat
Spring 2015
Quizz # 1 solutions
Solutions by Yury Kiselev
1. (25 points)
(a) (10 points) Lets set y = 0 at a position of the mass along vertical axis such that
the mass is at equilibrium. Lets nd how tota
Question
Define the Reynolds number Re for a viscous flow. YOU MAY ASSUME
that a suitable non-dimensional form of the steady Navier-Stokes equations
for use in studying boundary layer theory is
(q.)q = p +
1 2
q
Re
.q = 0
where the fluid pressure and velo
H.P. Paar
PHYS 4B: Mechanics, Fluids, Waves & Heat
Spring 2015
Quizz # 2 solutions
Solutions by Yury Kiselev
1. (15 points) Density of the water is higher than density of the ice, so a given volume of
the ice melts into a smaller volume of the water, so t
PHYSICS 4B
PROF. HIRSCH
QUIZ 4
3 Problems
SPRING QUARTER 2014
May 19th
Problem 1 (10 pts)
An ideal gas has 32,000 molecules moving with velocity in the x direction in the range
-1m/s to 1m/s, and 16,000 molecules moving with velocity in the x direction in
CHAPTER 18: Kinetic Theory of Gases
Responses to Questions
2.
The change in temperature when a gas is compressed or when it expands against a piston is due to
the increase or decrease in the average speed of the molecules. The increase or decrease in spee
PHYSICS 4B
PROF. HIRSCH
QUIZ 1
3 Problems
SPRING QUARTER 2014
APRIL 7th
Problem 1 (10 pts+2pts extra credit)
liquid
A cubic block of side length 10 cm and mass 100 g floats in a liquid (not water). Half of
the block is submerged. Ignore atmospheric pressu
CHAPTER 19: Heat and the First Law of Thermodynamics
Responses to Questions
26. At night, the Earth cools primarily through radiation of heat back into space. Clouds reflect energy
back to the Earth and so the surface cools less on a cloudy night than on
CHAPTER 20: Second Law of Thermodynamics
Responses to Questions
13. 1 kg of liquid iron will have greater entropy, since it is less ordered than solid iron and its molecules
have more thermal motion. In addition, heat must be added to solid iron to melt i
Question
A two-dimensional viscous unsteady flow takes place in the (x, y)-plabe. Ther
are no body forces. The fluid is incompressible and hsas constant density
and constant dynamic viscosity . Show that, when the Reynolds number
Re is much less than one
Question
Verify thet, if U is a constant, then the stream function (x, y) = U xy
represents two-dimensional inviscid flwo with no bsy forces in the region
cfw_(x, y) : (x 0), (y 0) bounded by solid walls at x = 0 and y = 0. Derive
the (dimensional) bounda
Question
An incompressible viscous heat-conduction fluid on constant density and
constant kinematic viscosity flows past a flat plate at y = 0. The flow is
two-dimensional. Far away from the plate, the speed of the fluid is (U, 0) T
where U is a constant.
Question
Incompressible viscous fluid of constant density and constant kinematic
viscosity occupies the region
cfw_ < x < , < y <
above an impermeable plane situated at z = 0. This plane creates flow in
the region z > 0 by moving with a speed U cos(t) pa
Question
BRIEFLY explain the difference between the Lagrangian and Eulerian
dscripitons of flow. A fluid occupies the region D(t), and at a time t =)
position vectores in D(0) are described by X = (X, Y, Z). At a later time t
position vectors in the fluid
Question
A viscous fluid of constant density and constant dynamic viscosity flows
steadily under gravity down a rigid impermeable plane. The acceleration
due to gravity is denoted by g. The plane is inclined at an angle to the
horizontal. The flow is two-
Question
A viscous fluid has constant density and constant kinematic viscosity .
Non-dimensionalise the steady Navier-Stokes equations with suitable scalings
to show that, when the Reynolds number Re satisfies
Re 1,
the non-dimensional equations of motion
Question
A viscous incompressible fluid (having constant density and constant kinematic viscosity ) flows steadily in a pipe of constant cros-sectional are which
has its generators parallel to the z-axis. There are no body forces. The crosssection of the
Question
A viscous incompressilbe fluid with constant density and constant dynamic
viscosity flows unsteadily in the (x, y)-plane. There are no body foces.
Show that when the Reynolds number Re is much less than one the flow is
governed by the SLOW FLOW E
Question
A viscous fluid of constant density and constant kinematic viscosity flows
steadily in a two-dimensional channel < x < , 0 z h. There are
no body fporces. Thwo solid planes at z = 0 and z = h confine the fluid
and flow is produced by a pressure g
Question
Two-dimensional fluid flow takes place in the first quadrant of the (x, y)plane. The stream function for the flow is given by
(x, y) = Cxy
where C is a positive constant.
(i) Determine the flow velocity components.
(ii) Show that the flow is irro
Question
A solid sphere r = a is held fixed in an otherwise uniform free stream of
speed U which flows parallel to the x-axis. The REynolds number of the
stream is small. The fluid has constant density and constant kinematic
viscosity and its velocity it
Question
(a) Give a brief explanation of the difference between Eulerian and Lagrangian
descriptions of a fluid flow. Denoting the Eulerian coordinates as usual
by x, prove that for any suitably smooth function (x, t)
d
= t + (q.)
dt
where q is the flow v
Question
An axisymmetric jet of viscous incompressible fluid of consatn density and
constant kinematice viscosity is injected in the positive z-direction through
a jole at r = z = 0 into the same fluid at rest. Cylindrical polar coordinates
(r, , z) are u
Solutions to problems on heat engines and
Carnot cycle
Problem 1
The theoretical maximum eciency of the heat engine is given by the eciency
of a reversible heat engine. For a heat engine operating between Th and Tc ,
Tc
this maximum eciency is emax = 1 Th
Solutions to problems from kinetic theory of gases
1
Problem 1
We assume the gas is an ideal gas whose velocities are distributed according to
the Maxwell-Boltzmann distribution for the speeds f (v). For a certain gas at a
specic temperature,
f (v)dv v 2