FLUID FLOW

1
FLUID FLOW

• TYPICAL ENGINEERING PROBLEMS
• given some inlet conditions, estimate the exit
  conditions from a system
• given the flow conditions, estimate the forces
  generated by the flow
• estimate the power generated or consumed by a
  flow system

2
FLUID FLOW

• ANSWERS PROVIDED BY
• THE APPLICATION OF THE THREE CONSERVATION
  EQUATIONS
• MASS ( CONTINUITY EQUATION)
• FORCE/MOMENTUM ( NEWTONS SECOND LAW OF MOTION)
• MECHANICAL ENERGY ( BERNOULLI EQUATION)

3
CONTROL VOLUME CONCEPT

• AN ARBITRARY VOLUME OF FLOWING FLUID
• BOUNDED BY A COMPLETELY POROUS CONTROL SURFACE
• CONSTRUCT BALANCES ON THE FLUID IN THE CONTROL
  VOLUME

4
CONSERVATION OF MASS

• usually referred to as the CONTINUITY EQUATION
• MASS FLOW OUT MASS FLOW IN PLUS ACCUMMULATION
  (OR LOSS) OF MASS WITHIN THE CONTROL VOLUME

5
CONTINUITY

• STEADY STATE FLOWS
• m ? 1U1A1 ?2U2A2 kg/s
• INCOMPRESSIBLE FLOWS
• LIQUIDS AND LOW SPEED GASES
• Q U1A1 U2A2 m3/s

6
FORCE-MOMENTUM BALANCE

• NEWTONS SECOND LAW OF MOTION
• APPLIED TO FLUID IN A CONTROL VOLUME
• SUM OF FORCES ACTING ON THE CV
• RATE OF CHANGE OF MOMENTUM OF THE FLUID IN THE CV
• RATE OF CHANGE OF MOMENTUM
• MOMENTUM FLOW OUT - MOMENTUM FLOW IN

7
FORCE-MOMENTUM BALANCE

• APPLY IN A FIXED DIRECTION
• BE RIGOROUS WITH SIGN CONVENTION
• MOMENTUM FLOW MASS FLOW RATE X VELOCITY

8
FORCE- MOMENTUM BALANCE

• EXAMPLES OF APPLICATION
• JET IMPACT
• JET THRUST

9
FORCE-MOMENTUM BALANCE

• FORCES ON STATIONARY EQUIPMENT
• THE NOZZLE
• THE PIPE REDUCER
• THE BEND

10
FORCE-MOMENTUM BALANCE

• FORCES ON MOVING EQUIPMENT
• THE TURBINE BLADE

11
THE GENERAL FLOW PROBLEM

• CONTINUITY
• FORCE-MOMENTUM
• BERNOULLI