1. Chap. 6: Applications of Macroscopic Balances
1. Introduction
• Conservation of mass, energy, & momentum
Simplified version at steady states
Ex.) Expansion losses in
No. of unknowns > No. of eqn.
(p1-p2) or F must be known

2. • Simpler applications
Case I: Viscous losses for a given flow
P from EOM  Losses from EOE
(prior information F)
Case II: Force for a given flow
P from EOE  Force from EOM
(prior information viscous losses)
Case III: Pressure change for a given flow
Known F  P from EOM or
Known viscous losses  P from EOE

3. 2. Losses in Expansion
• Losses in flow of an incompressible fluid through
an expansion
(Table 5-1)
• P from EOM  Losses from EOE
• Assumption: turbulent, uniform velocity over cross-section
at positions 1 and 2 (==1)
F component in flow direction
Fluid pressure on the expansion
surface at plane “e”
Let’s decompose F:
Tangential friction drag
along the walls
(Pe: gage pres., outside pres.=0)

4. pep1
(small distance)
(pep1, short segment, Ve=V1)
• From Bernoulli eq.
Borda-Carnot eq.:
(See Table 5-1)

5. 3. Force on a Reducing Bend
Horizontal reducing bend
3. Force on a Reducing Bend
• Force necessary to maintain
a 90o reducing bend
• P from EOE  Force from EOM
• Incompressible fluid, turbulent
(flat velocity, ==1, <V>=V),
no shaft work
(No gravity in xy-plane)

6. 4. Jet Ejector Uniform Vs & Vj at pt. 1 Uniform velocity at pt. 2
(p2 - p1) (positive ?)

7. (No gravity, F=0)

8. 5. Flow through an Orifice
• Q & p ?
• p from EOM or EOE (but, from EOE here
due to difficulty to measure F)
• One of flow measuring systems
e.g., venturi meter, rotameter, turbine meter
• Incompressible, uniform velocity

9. 6. Pitot Tube (stagnation pt.) • Velocity profiles in a flowing system
by means of pressure measurement
• p from Bernoulli eq.
(stagnation pres.)
• Useful for high Re condition (viscous terms should be considered at low Re)

10. Re=1.2*105
Re=800

11. (valid for 50 < Re < 100)
7. Diameter of a Free Jet
Laminar flow
Uniform velocity
Negligible
(valid for 50 < Re < 100)

12. 8. Manifold Negligible Horizontal Horizontal Negligible
Pressure recovery
Negligible
Horizontal
Horizontal
Negligible
Side flow