Fm Unit 3 Formula

7/25/2019 Fm Unit 3 Formula

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UNIT-III (Formulae)

Fluid Dynamics

+ + = = = =

+

2 + =

+

2 +

It states that in an ideal fluid incompressible fluid when the forces is steady and

continues, the sum of pressure energy, kinetic energy and potential energy is constant along a

stream line.

Assumptions;

1.

The liquid is ideal and incompressible

2.

Flow is steady and continuous

3.

Flow is along the stream line (i.e one dimensional )

4.

Velocity is uniform over section and is equal to mean velocity.

5.

The forces acting on fluid are gravity force and pressure force.

Application of Bernoullis Equation:

1.

Venturimeter

2.

Orifice meter (or) Orifice plate

3.

Pitot-tube

Venturimeter : a1-area at inlet of Venturimeter

Actual discharge (Qact) = a2-area at throat of venturimeter

Theoretical discharge (Qth) =

=

Cd - co-efficient of discharge

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(i)

When venturimeter Horizontal ( Sm> S)

= = 1x= Difference of the heavier liquid column in U-tube

(ii)When venturimeter vertical and inclined (Sm> S)

= 1x= Difference of the heavier liquid column in U-tubePressure difference between entrance and throat section (p1-p2)

= + +

Orificemeter:

Actual discharge (Qact) = 2

Where, a0= Area of Orifice

a1= Area of inlet section

g= acceleration due to gravity (9.81 m/s2)

h = differential U- tube manometer

Pitot tube:

=




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Flow of viscous fluid in circular pipe and parallel plate Hagen poiseuille law:

(i)

Shear stress = (ii)

Velocity distribution = (iii)

Average velocity = (i)

Maximum velocity= ()

Ratio of velocities (or) Maximum velocity to average velocity()

= 2(i) Loss of pressure (Or) Loss of drop

=

(ii)

Loss of pressure head

= = Where,

= pressure gradient, r =radius at any point

R= radius of the pipe D= Diameter of the pipe

= average velocity = Q/R2




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2 marks

Fluid Dynamics

1.

What are the forces present in a fluid flow?

Fg-Gravity force

Fp-Pressure force

Fv-Force due to viscosity

Ft-force due to turbulence.

Fc-Force due to compressibility.

2. Give the Eulers equation of motion?

+ . + = 0

3. State Bernouillies theorem?

It states that in a steady ideal flow of an incompressible fluid the total energy at any point of

the fluid is constant. The total energy consists of pressure energy, Kinetic energy and potential

energy is to be consent.

+

2+ =

4. What are the assumptions made in deriving Bernouillies equation?

a. The fluid is ideal and incompressible

b. The flow is steady and continuous

c. The flow is irrotational.

d.

5. State the application of Bernouilliesequation ?

It has the application on the following measuring devices.

(i)

Orifice meter.

(ii)

Venturimeter.

(iii)

Pitot tube.

6. Define venturimeter?

A venturimeter is a device used for measuring the rate of flow of a fluid flowing through

a pipe. It consists of three parts, they are short converging part, and throat a diverging part.




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7. What purpose orifice meter is used? Define it?

It is a device used for measuring the rate of flow of a fluid through a pipe.Orificemeter

consist of a flat circular plate which has a circular sharp edged hole called orifice meter.

8. Define pitot tube and give its working principle?

The pitot tube consist of a glass tube bent at right angles.It is based on the

principle that if the velocity of flow at a point becomes zero the pressure there is

increased due to conversion of kinetic energy into pressure energy.

9. Define Momentum principle

The net forces acting on a mass of fluid is equal to the change in momentum of flow per

unit time in that direction.

10.What are the factors to the determined when viscous fluid flows through the circular

pipe?

The factors to the determined as

i. Velocity distribution across the section.

ii. Ratio of maximum velocity to the average velocity .

iii. Shear stress distribution.

iv. Drop of pressure for a given length .

11.What do you meant by viscous (or) laminar flow ?

A flow is said to be viscous if the Reynoldss number is less than 2000 (or) the

flowsin layers ie. Re


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13.

Derive the relation between maximum velocity Umaxand average velocity?

=

= 14.Give the equation for average velocity : -

The equation for average velocity is given as

= 18

Where R = Radius of the pipe

15. Give the formula for velocity distribution: -

The formula for velocity distribution is given as

= 14 Where R = Radius of the pipe

r = Radius of the fluid element

16.What are the assumptions made in Hagen Poiseuilles Law?

(i) The fluid follows Newtons law of viscosity

(ii) There is no slip of fluid particles at the boundary (the fluid particles adjacent to the

pipe will have zero velocity)

17.

State momentum equation and Impulse momentum equation?The momentum equation states that net force acting on a fluid mass in equal to

the change in momentum per second in direction. This is given as

F=d(mv)/dt

The impulse momentum equation is given by F.dt=d(mv)

Prepared by:S.MANIMARAN

Asst.Prof

Dept of Civil Engg.,

TRP Engg. College

Trichy.



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Fm Unit 3 Formula