2014/15
TUTORIAL 3
FLUID STATICS
1. A manometer is connected to two points on a tube with a pressure difference 1200 Pa. The tube
contains a liquid of density 1000 kg/m3, while the manometer contains a second liquid of density
3000 kg/m3. Calculate the he
2014/15
TUTORIAL 2
VISCOUS FORCE
1. Deduce from Newtons law of viscosity the units of viscosity and kinematic viscosity.
2. Find, from a book or from the internet, the viscosity of:
a) water at 20, 30,. 100oC
b) air (P = 1 atm) at 20, 30,. 100oC
What do y
2014/15
TUTORIAL SHEET 4
FLOWRATE AND FLUX, REYNOLDS TRANSPORT THEOREM, CONSERVATION OF MASS
1. The following velocity profile describes a flow between two horizontal, stationary parallel plates, where y
is the vertical axis, h is the distance separating
TUTORIAL SHEET 5
CONSERVATION OF MOMENTUM
2014-15
1. A horizontal round jet of liquid of density , uniform velocity u and volumetric owrate Q ows
steadily onto a at plate of area A which is held stationary, normal to the axis of the jet, by a
bracket. An
2014/15
TUTORIAL 1
VELOCITY FIELD, STREAMLINES AND PATHLINES
1. For the velocity fields below, determine:
a) whether the flow field is one-, two- or three-dimensional, and why.
b) whether the flow is steady or unsteady, and why.
(1) = ( + )
(4) = + 2 +
(
Lecture 19
Turbulent ow in pipes
Tutorial sheet 7: Problems 1-3
Turbulence: The Basic Questions
What is turbulence?
Turbulence: The Basic Questions
What is turbulence?
What causes turbulence?
Turbulence: The Basic Questions
What is turbulence?
What causes
Mathematics supplement for ME1 uid mechanics
The following covers some mathematical techniques that we will need for ME1 uid mechanics
and students, due to their variable background, may or may not have seen before.
An equation of the type:
f
dy
, y, x
dx
Lecture 17
Conservation of energy
The pipe ow energy equation
Tutorial sheet 6: All problems
The Conservation of Energy Equation
Conservation of energy has been discussed extensively in your
thermodynamics course (First Law for open systems)
We will deriv
Lecture 15
The Bernoulli equation
Examples
Tutorial sheet 6: Problems 1-4
The Bernoulli Equation
One of the most well-known equations of uid mechanics
Subject to important assumptions
Derivation by applying Newtons law to a uid particle, rather
than via R
Lecture 12
Methodology for problem solving with
conservation of momentum
Examples
Tutorial sheet 5: Problems 1,2,3,6
Summary of equations useful for problem solving:
Steady ow, integral form:
uu d A =
F
CS
Resolved into: (for 2-D Cartesian coordinates)
uu
Lecture 14
Further examples on conservation of momentum - drag force
Tutorial sheet 5: All problems
Example 3: Drag Force
The drag force is the force resisting the motion of a solid object through
a uid. A model is placed within a steady ow of air in a wi
Lecture 16
The Bernoulli equation - further
discussion
Further examples
Tank draining
Tutorial sheet 6: Problems 1-4
Example 2: Tank Draining
A tank is draining from an orice at the bottom. If the height of the
water is h, derive an expression for the dis
Lecture 13
More examples on conservation of
momentum
Two dimensions
Moving frame of reference
Tutorial sheet 5: All problems
Example 2: Moving Control Volume
Given:
Constant cart velocity, uniform jet velocity and cross-sectional area,
magnitude of jet ve
Lecture 11
Conservation of momentum
Notes:
SOLE comments
ME1 Thermouids laboratory
Tutorial sheet 4: All problems
Can start looking at tutorial sheet 5
SOLE comments
Many favourable comments - thank you!
Material is interesting and intellectually stimulat
Lecture 10
The Reynolds Transport Theorem
Conservation of mass
Tutorial 4: All problems
Lecture notes part II will be delivered next week (also available
on moodle)
Five Basic Questions
What is a uid?
How do we describe mathematically the motion of uids?
Lecture 8
Buoyancy
The fundamental laws of fluid mechanics
System and control volume approach
Flowrate and flux
Tutorial 3: All problems
Progress test
Theory: up to (and including) flowrate and flux (p. 56 in the notes)
Problems: tutorial sheets 1-3
Bu
Lecture 9
Flowrate and flux conclusion
Revision
Tutorial 4: problems 1 & 2 (not included in the
progress test)
Notes
SOLE please give us your feedback
Example 2: More complex surface
Find the mass flowrate through the surface shown below (constant dens
Lecture 7
Hydrostatic forces on flat surfaces
The surface integral
Hydrostatic forces on curved surfaces
Tutorial 3: Fluid statics (problems 4-6)
Hydrostatic forces on flat surfaces
Pressure on a submerged surface is a distributed force
How to calcu
Lecture 4
Forces in fluids
Body and surface forces
Viscous force
Tutorial 2: Viscous force
Note:
Mechanics of Fluids by B. Massey now
available in the library as an ebook
The story so far
Fluids, unlike solids, cannot sustain a shear force at rest
Des
Lecture 6
Classification of fluid flows
Hydrostatic equation
Manometers
Tutorial 3: Fluid statics (problems 1-3)
Note:
Mathematics supplement available on
moodle
Forces in fluids - summary
There are four main forces in fluids: gravity, pressure, visc
5. CURVE SKETCHING
There are many situations where it is very useful to be able to determine roughly
the behaviour of a function, without plotting it out in detail. For example, to obtain
estimates of the roots of nonlinear algebraic equations to serve as
Lecture 5
More on viscous force
Pressure
Tutorial 2: Viscous force
Note:
Lecture slides now on moodle
Newtons law of viscosity says that viscous stress is proportional to
velocity gradient:
=
This law is verified experimentally for a large class o
Polar Co-ordinates
63
Example
64
6. HYPERBOLIC FUNCTIONS
The exponential function, ex, is neither even nor odd, but can be arranged as the
sum of an even and an odd function in the usual way
ex =
e x + e x e x e x
+
2
2
even
odd
The even function so f
Lecture 3
Streamlines
Pathlines
Tutorial 1: Velocity field, streamlines and
pathlines
Streamlines
How to visualise the velocity field?
Plot a vector at each point
Streamlines
A streamline is a line to which the velocity vector is tangent at all
poi