Blackboard lecture 2

1. Instrument Measurement
Principles
PHYS6008

2. Flow Measurement
Section 2

3. Learning Objectives
• When this section is completed the learner
will be able to:
• Describe an Ideal fluid
• Describe and calculate : Volume Flow Rates
and Mass Flow Rates
• Derive and Apply the Equation of Continuity

4. What is an ideal fluid?
1. Fluid is non-viscous (no friction to dissipate
energy)
2. Fluid is incompressible (no density change in
the pressurised fluid)
• Assumption number 2 only holds in reality for
liquids.
• We shall consider the velocity of flow to be
constant across a section of pipe.

5. DOES AN IDEAL FLUID EXIST?

6. Volume Flowrate Fv
• Volume Flow Rate, Fv, is the volume of fluid passing
through a section [in e.g. a pipe] per second.
• Consider fluid flowing at velocity v in a pipe of cross-
sectional area A.
• What volume of fluid passes through section X of
Area A in 1s?

7. Volume Flowrate Fv

8. Mass Flowrate Fm

9. Flowrate Examples 2 & 3
See : Flowrate Examples 2&3.pdf for solutions

10. Equation of Continuity
• If a fluid is flowing along a tapering pipe
where the cross sectional area A is
changing, its velocity v will change from one
location to another.

11. Equation of Continuity
Let ρ = fluid density
v1 = velocity of fluid at 1
v2 = velocity of fluid at 2
A1 = cross sectional area of pipe at 1
A2 = cross sectional area of pipe at 2

12. Equation of Continuity

13. Equation of Continuity

14. Example 4
Water flows through a horizontal pipe of radius
10 cm at a velocity of 2 ms-1. The water then
flows through the constriction of radius 3 cm.
Find:
(a) the volume flow rate through the pipe,
(b) the velocity of the water through the
constriction.