3.1 CONTINUITY EQUATION : FLUID MOMENTUM, BERNOULLI EQUATION FOR FRICTIONLESS FLOW, RELATION BETWEEN PRESSURE AND VELOCITY.








flow often referred as an ideal fluid.
-presume has no viscosity.





Real fluid-is the effects of viscosity are introduced into the problem.














Incompressible fluid flow- fluid has constant density
                      ( ρ=constant)

Types of flow:-
1.
Steady flow
-steady with respect to time
-flow at every point remain constant with respect to time
2.
Uniform flow
-when the cross-section(shape and area) through the flow occurs remains constant.


Path line- path line shows the direction of the velocity.



Stream line- mean direction of number of particles at instant time.

Flow rate = quantity of fluid flowing per unit time cross any section.

VOLUME FLOW RATE (Q)

Q=Av         where A= area of section(m2)
                   v=average velocity of the flow (m/s)

Unit: SI -m3/d

MASS FLOW RATE (m)

  m=ρQ

 Where, ρ=density(kg/m3)
       Q=volume flow rate(m3/s)
Unit: SI -kg/s

WEIGHT FLOW RATE

  G=ɣQ

 Where, ɣ= specific weight (N/m3)
        Q= volume flow rate (m3/s)
Unit: SI - kN/s


                                                EQUATION OF CONTINUITY





Incompressible flow (ρ=constant)

A1V1=A2V2=Q 



                                              BERNOULLI EQUATION

-Approximate realtion between pressure , velocity , and elevation.
-it has been proven to be a very powerful tool in fluid mechanics.
-combined effects of pressure and gravity forces.


One-dimensional Euler Equation :



    

(equation 3.3)






INCOMPRESSIBLE FLUID (ɣ= constant )






  Where , p=pressure
         Ɣ=specific weight
         z= height
         v=velocity
         g= gravity



















                                

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