This document discusses different types of fluid flow and equations related to fluid flow. It contains the following key points: 1) Laminar flow occurs when layers of a fluid flow smoothly past one another, while turbulent flow involves irregular particle movement. 2) The continuity equation states that the rate of fluid entering a pipe must equal the rate leaving, so mass is conserved. 3) Bernoulli's equation relates pressure, velocity, and height of an incompressible fluid in static equilibrium, such that the total mechanical energy at each point remains constant as fluid flows.

1. Y.Bavaneethan
Lecturer
Department of Food Technology.
SLGTI, Sri Lanka
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2. Laminar and Turbulent Flow
The flow in which in each point occupied by fluid its velocity
doesn’t change in time is called stationary flow.
Laminar flow
If the flow is smooth, such that neighbouring layers of the fluid
slide by each other smoothly, the flow is said to be streamline or
laminar flow.
Hence all particles have a velocity only in the direction of flow.
Turbulent Flow
The particles move in an irregular manner through the flow
field.
Each particle has superimposed on its mean velocity fluctuating
velocity components both transverse to and in the direction of
the net flow.
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3. (a) = Laminar flow
(b) = Turbulent flow7/6/2018 Y.BAVANEETHAN 3

4. Continuity equation for a fluid
 In such a pipe, the mass must be conserved,
e.g. if we put mass m1 into the pipe,
• Then the same mass m2=m1 must flow out of this pipe
• Provided, the fluid is incompressible,
• Otherwise the pipe can accumulate some mass, with no
outgoing flow.
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5. Conservation of Mass: The Continuity Eqn.
The rate a fluid enters a pipe must equal the rate the fluid leaves the pipe.
i.e. There can be no sources or sinks of fluid.
“The water all has to go somewhere”
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6. Volume, that falls into the pipe in a time dt(a sec) is equal,
V=Adx,
• where A is the area of crosssection of the pipe,
• dx is the thickness of the mass layer, pumped in time dt (a
sec)
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7. Calculations
01] A liquid flows through a pipe with a diameter of 10cm at a velocity
of 9cm/s. If the diameter of the pipe then decreases to 6cm, what is the
new velocity of the liquid? (25cm/s)
02] A pipe with a diameter of 2cm is attached to a garden hose with a
nozzle. If the velocity of flow in the pipe is 2m/s, what is the velocity
of the flow at the nozzle when it is adjusted to have a diameter
of 4mm?
(50 m/s)
03] If a pipe with flowing water has a cross-sectional area nine times
greater at point 2 than at point 1, what would be the relation of flow
speed at the two points?
Possible Answers:
1. The flow speed at point 2 is nine times that at point 1
2. The flow speed at point 2 is three times that at point 1
3. The flow speed at point 1 is three times that at point 2
4. The flow speed at point 1 is nine times that at point 2
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8. 04] As water is traveling from a water tower, to somone's home, the
pipes it travels in frequently change size.
Water is traveling at 5m/s in a tube with a diameter of 0.5m. The tube
gradually increases in size to a diameter of 1.5m, and then gradually
decreases to a diameter of 1m. Neglecting any energy losses due to
friction and pressure changes, what is the speed of the water when it
reaches the tube diameter of 1m?
05] Blood travels through an artery at velocity V. If a vaso
constricting chemical is consumed and the artery constricts to
half the original diameter, what is the new velocity of the blood?
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9. Conservation of Mass: The Continuity Eqn.
Q. A river is 40m wide, 2.2m deep and flows at 4.5 m/s. It passes
through a 3.7-m wide gorge, where the flow rate increases to 6.0
m/s. How deep is the gorge?
𝐴1 = 𝑤1 𝑑1
𝐴2 = 𝑤2 𝑑2
𝐶𝑜𝑛𝑡𝑖𝑛𝑢𝑖𝑡𝑦 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 ∶ 𝐴1 𝑣1 = 𝐴2 𝑣2 → 𝑤1 𝑑1 𝑣1 = 𝑤2 𝑑2 𝑣2
𝑑2 =
𝑤1 𝑑1 𝑣1
𝑤2 𝑣2
=
40 × 2.2 × 4.5
3.7 × 6.0
= 18 𝑚
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10. The relationship between pressure and velocity in fluids is described
quantitatively by Bernoulli’s equation.
Bernoulli’s equation states that for an incompressible, frictionless fluid, the
following sum is constant:
A fluid can also change its
height. By looking at the work
done as it moves, we find:
This is Bernoulli’s equation.
One thing it tells us is that as
the speed goes up, the pressure
goes down.
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Bernoulli’s Equation
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11. v2Dt
v1Dt
constvpvp  2
22
1
2
2
12
1
1 Energy per unit
volume
y1
y2
1yg 2yg
Total energy per unit volume is constant
at any point in fluid.
constygvp   2
2
1
P = Absolute pressure
ρ = Fluid density
V = Velocity of the fluid
h/y = Height above the reference point.
g = Acceleration due to gravity.
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12. Bernoulli’s Eqn.
Q. Find the velocity of water leaving a tank through a hole in the side 1
metre below the water level.
𝑃 + 1
2
𝜌𝑣2 + 𝜌𝑔𝑦 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝐴𝑡 𝑡ℎ𝑒 𝑡𝑜𝑝: 𝑃 = 1 𝑎𝑡𝑚, 𝑣 = 0, 𝑦 = 1 𝑚
𝐴𝑡 𝑡ℎ𝑒 𝑏𝑜𝑡𝑡𝑜𝑚: 𝑃 = 1 𝑎𝑡𝑚, 𝑣 =? , 𝑦 = 0 𝑚
𝑃 + 𝜌𝑔𝑦 = 𝑃 + 1
2 𝜌𝑣2
𝑣 = 2𝑔𝑦 = 2 × 9.8 × 1 = 4.4 𝑚/𝑠
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13. Importance of viscosity / fluid flow in the food
industry.
• Viscosity measurements are used in the food industry to
maximize production efficiency and cost effectiveness.
• It affects the rate at which a product travels through a pipe,
• How long it takes to set or dry, and
• Time it takes to dispense the fluid into packaging.
• The production process designed with the viscosity of the
product,
• Pipes are angled to optimize flow, or
• dispensers provide the right amount of force to induce flow
• Viscosity is also a characteristic of the texture of food.
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14. THANK YOU
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