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Practical 1: Fluid Flow in a Smooth Pipe
Aims
1. To investigate the variation in pressure drop with the volumetric flow rate of water in a circular
pipe
2. To construct a plot of friction factor versus Reynolds number
3. To observe the transition from laminar flow to turbulent flow by injecting a dye into water flowing
in a pipe
4. To observe various types of pressure gauges in operation
Scenario
You have started working as a graduate engineer in a company which manufactures pipelines. The first
task given to you by your boss is to study the correlation between the Fanning friction factor and the
Reynolds number of water flowing in a pipe and therefore, construct a Moody diagram. To complete
this task, you have been given access to the company’s laboratory, where you will conduct scientific
experiments to achieve your goal. In particular, you will have access to pressure gauges, flow meters,
and a straight glass pipe. A description of the apparatus is provided below:
Pressure Gauges
A pressure gauge is used to measure pressure by analysing the force applied by a fluid on a surface.
Various types of pressure gauges are used to measure different pressure ranges. In the laboratory, you
will have access to a inverted water-air manometer (inclinable; measures up to 5 kPa), and a wet-wet
digital pressure gauge (measures up to 100 kPa). You will need to choose the appropriate pressure
gauge to ensure accuracy. To measure the pressure, simply read off the pressure reading when using the
wet-wet digital pressure gauge. For the inverted inclinable water-air manometer, you will need to use
hydrostatic pressure concepts to calculate the pressure difference. The resolution of the wet-wet digital
pressure gauge is 0.1 kPa, while the manometer scale has 1 mm demarcations and is inclinable in 15
degree increments from vertical to horizontal.
Flow Meters
A flow meter is used to control the flow rate of a fluid. You will have access to three rotameters which
can control water flow rates up to 70, 250, and 1600 L/h respectively. A rotameter is an example of a
variable area flow meter, where a weighted float rises in a tapered tube as the flow rate increases. The
floatstopsrisingwhentheareabetweenthefloatandthetubeislargeenoughfortheweightofthefloat
to be balanced by the drag of fluid flow. Rotameters are available for a wide range of liquids but are
most commonly used with water or air. They can reliably measure flow down to 1% accuracy.
Pipe
In the laboratory, you will also have access to a glass pipe which is 12.6 mm in diameter and 1.5 m in
length.
1
Figure 1: The two types of pressure gauges in the laboratory. (a) inverted water-air manometer and (b)
wet-wet digital pressure gauge.
Figure 2: (a) A rotameter to be used in the experiment. (b) A schematic diagram of a rotameter. The
flow of liquid creates an upward force opposing the weight of the float, creating an equilibrium
situation such that the float will remain stationary to indicate the flow rate.
Task
You will conduct experiments to measure pressure drop values that correspond to various volumetric
flow rates between 0 to 1600 L/h for the flow of water in a straight glass pipe. You should consider the
following when writing up your experimental protocol and constructing your schematic diagram:
? Are there any safety checks or calibrations required before switching on the pressure gauges and
flow meters?
? What are the parameters to be measured in this experiment?
? What calculations are required to obtain the Fanning friction factor and Reynolds number?
2
? How many flow rates should you run for each of the three flow meters?
? Should you start the pipe flow at a high or low flow rate? Why?
? How do you decide the type of pressure gauge to use in order to maintain accuracy? Why is the
inclinable feature of the inverted water-air manometer useful and when/how should this be used
to maintain accuracy?
? Show all pipelines and how the experimental apparatus are connected in the schematic diagram
? Think about how the different pressure gauges should be connected to the pipe
? Again, think about how the flow meters should be connected to the pipe. Should they be put
towards the start or the end of the pipe? Why?
Theory
For fluid to flow in a pipe, a driving force in the form of a pressure drop (?P) is required. The pressure
drop required depends on the average velocity (V), fluid density (ρ), fluid viscosity (μ), pipe diameter
(D), and pipe length (L). The pressure change in a fluid under steady-state flow conditions is described
by the mechanical energy balance:
P 1 P 1
1 + V2+z = 2 + V2+z +h
ρg 2g 1 1 ρg 2g 2 2 L
In the equation above:
? P: pressure in the fluid
? ρ: density of the fluid
? g: acceleration due to gravity
? V: velocity of the fluid
? z: elevation of the fluid
? h : head loss due to friction
L
For flow in a horizontal pipe at a constant velocity, z =z and V =V . Therefore, it follows that:
1 2 1 2
P ?P
h = 1 2
L ρg
Thatis,thedropinpressureisduetofluidfrictionaloneandisnotduetochangesinkineticorpotential
energy.
The head loss (h ) may also be expressed in terms of a Fanning friction factor (f ):
L F
2f LV2
h = F
L Dg
Experimentation has shown the following to be true for fluid flow in a smooth horizontal pipe:
1. The head loss varies directly with the length of the pipe
2. The head loss varies almost directly with the square of the velocity
3. The head loss varies almost inversely with the diameter of the pipe
4. The head loss depends on the fluid’s properties (density and viscosity)
5. The head loss is independent of pressure
3
The Fanning friction factor (f ) is a function of fluid velocity (V), pipe diameter (D), fluid density (ρ),
F
and fluid viscosity (μ), and the only way to make it dimensionless is as follows:
(cid:16)ρVD(cid:17)
f =f
F μ
The group ρVD is known as the Reynolds number. Hence, the Fanning friction factor is a function of
μ
only the Reynolds number.
When the flow rate through the pipe is low, the flow pattern is smooth and steady. A dye solution
carefully injected into the pipe will trace out a straight line. This orderly flow is referred to as laminar
flow. As the flow rate increaseds the stream of dye loses its steadiness and begins to vacillate. This
vacillation increases as the velocity of the fluid increases. At sufficiently high velocity, the dye solution
no longer retains its identity and is dispersed across the pipe. It becomes completely mixed with the
surrounding liquid, and the flow pattern is no longer steady and smooth - it has become chaotic. The
flow is now said to be turbulent.
The transition from laminar to turbulent flow occurs at different velocities for different fluids and differ-
ent pipe sizes. However, when expressed in terms of Reynolds number, the transition occurs at a fairly
well-defined Reynolds number value. This is known as the critical Reynolds number for pipe flow. In
this experiment, the critical value may be determined by observing the gradual change to a disordered
state of a line of dye injected into the centre of a flowing water stream.
The flow patterns of laminar, transitional, and turbulent flow will be demonstrated by injecting a dye
into the water flow channel at various flow rates.
