Flow of Fluids and Bernoulli's Equation

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B Y : M D M . N A D I A B I N T I M O H A M E D

FLOW OF FLUIDS ANDBERNOULLI¶S EQUATION

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TYPES OF FLOW LINES

y Uniform Flow.

 A flow , in which velocities of liquid particles at allsections of the pipe or channel are equal, is called a

uniform flow. This term is generally applied to flow in channels.

y Non-uniform Flow.

 A flow , in which the velocities of liquid particles atall sections of the pipe or channel are not equal, iscalled a non-uniform flow.

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y Streamline Flow 

 A flow, in which each liquid particle has a definitepath and the paths of individual particles do not

cross each other, is called a streamline flow. It is alsocalled a laminar flow.

y Turbulent Flow 

 A flow, in which each liquid particle does not have adefinite path, and the paths of individual particlesalso cross each other, is called a turbulent flow.

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y Steady Flow 

 A flow , in which the quantity of liquid flowing persecond is constant, is called a steady flow. A steady 

flow may be uniform or non-uniform.

y Unsteady Flow 

 A flow, in which the quantity of liquid flowing persecond is not constant, is called unsteady flow.

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 Laminar and turbulent flow

y If we were to take a pipe of free flowing water andinject a dye into the middle of the stream, what

 would we expect to happen?

This

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This

This

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y  Actually both would happen - but for different flow rates. The top occurs when the fluid is flowing fastand the lower when it is flowing slowly.

y The top situation is known as turbulent f low and the lower as laminar f low .

y In laminar flow the motion of the particles of fluid is very orderly with all particles moving in straight

lines parallel to the pipe walls.

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y But what is fast or slow? And at what speed does theflow pattern change? And why might we want toknow this?

y The phenomenon was first investigated in the 1880s by Osbourne Reynolds in an experiment which has become a classic in fluid mechanics.

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y He used a tank arranged as above with a pipe taking water from the centre into which he injected a dy ethrough a needle. After many experiments he saw thatthis expression

y  Where = density, u = mean velocity, d = diameter and  µ= viscosity

y  would help predict the change in flow type. If the value is

less than about 2000 then flow is laminar, if y greater than 4000 then turbulent and in between these

then in the transition zone.

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y This value is known as the Reynolds number,

Re:

y Laminar flow: Re < 2000y Transitional flow: 2000 < Re < 4000

y Turbulent flow: Re > 4000

y  What are the units of this Reynolds number?

y It has no units. A q uantity  that has no units isk nown as a non-dimensional (or dimensionless)

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y  We can go through an example to discover at what velocity the flow in a pipe stops being laminar.

y If the pipe and the fluid have the following

properties:y  water density  = 1000 kg/m3

y pipe diameter d = 0.5m

y (dynamic) viscosity, µ = 0.55x10-3 Ns/m2

y  What is the maximum velocity when the Re is 2000.

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 Answer

Re: