FLUID FLOW
Fluid FLOW is about thesteady flow of fluid.
New concepts
1. Definition of steady-state flow
2. Mass and volume flow rates -continuity equation (what goes in must come out)
3. Bernoulli equation - conservation of energy of steady flow of fluid
4. Losses and "head"
Flow Rates
What goes in must come out
Steady flow means the fluid properties are constant - constant pressure, velocity, temperature etc.
Volume Flow Rate= V / t = A
Where
= volume flow rate or volumetric flow rate (m3/s). This may need to be converted from L/s (litres per second) or m3/h etc.
V = volume (m3)
= average velocity of the fluid (m/s)
A = cross-section area of the pipe (m2)
Mass Flow Rate = m / t = A
Where
= mass flow rate(kg/s)
m = mass of fluid (kg)
t = time (s)
= average velocity of the fluid (m/s)
= density of the fluid (kg/m3)
Continuity The continuity equation says that mass is conserved. (The mass that goes in) = (The mass that comes out).
in = out = constant
If the density is constant (OK for liquids, sometimes for gases), then
in = out = constant
Head In this example, HEAD isthe height of water above a turbine or pump, and is a way of measuring pressure.
An example of potential head (as in potential gravity). However, head means more than just pressure. The velocity of the flow can also raise the fluid to a height (head), and also the pressure has an equivalent head.
There are 3 types of head:
1. Pressure Head is the height to which a fluid will rise because of its pressure.
hp = p /g
hp = head (m)
p = pressure (Pa)
= density (kg/m3)
g = gravitational acceleration (9.81 m/s2)
2. Velocity Head is the height to which a fluid will rise because of its velocity.
hv =2 / 2g
hv = head (m)
= average velocity of the fluid (m/s)
g = gravitational acceleration (9.81 m/s2)
3 .Potential Head is the height of the fluid. (above a certain datum)
TOTAL head = sum of pressure, velocity and potential heads; H = hp + hv + h
Bernoulli Assumptions; An ideal fluid (no friction) flowing steadily...
· The fluid is incompressible and non-viscous
· There is no energy loss due to friction between the fluid and the wall of the pipe.
· There is no heat energy transferred across the boundaries of the pipe to the fluid as either a heat gain or loss.
· There are no pumps in the section of pipe under consideration.
· The fluid flow is laminar and steady state.
H = constant
The Bernoulli Equation is basicallythe conservation of energy along a pipe. It can be written in different ways by converting energy to head (Kinsky) orpressure, etc.
PRESSURE DENSITY... Here is the Bernoulli equation in terms of PRESSURE per unit volume;
HEAD... Here is the same equation in terms of HEAD. (Just divide the previous equation by g Kinsky Eqn 11.4, p241
· All terms are head (m).
· You can usegauge or absolute pressure throughout, but gauge is normal
· Continuity equation is also true (and usually needed to solve the question)
· Ideal fluid is assumed (no friction)
Special Cases: Some examples of the application of the Bernoulli Equation.
1. Horizontal Pipe: No potential head change so they cancel each other out.
2. A liquid surface is at atmospheric pressure. Pressure head at surface = 0 (gauge). Assume point 1 is the surface, then...
3. A nozzle discharges to atmosphere. Pressure head at outlet (2) = 0.
4. Pipe is parallel (constant diameter). No change in velocity, so velocity head cancels out.
5. Liquid flow in/out a large tank/lake. The velocity at surface is zero. For example, flow of a tap from a large tank...
Bernoulli with Head Loss
Head loss is the amount of TOTAL HEAD lost between points 1 and 2.
HL = H1 - H2
Interestingly, when losses occur in a pipe they do not affect every term in the Bernoulli equation, but only pressure.
· Potential: No change because the pipe still has the same start and end heights.
· Velocity: No change because the pipe still has the same start and end velocities (otherwise continuity is false)
· Pressure: Head loss will reduce the pressure!
Where HL = Total head loss
Questions:
Homework Assignment: Kinksy new edition
Do all questions; Chapter 11: Fluid Flow
11.1 to 11.20 (page 251-253)