Page 240 - Bird R.B. Transport phenomena

224 Chapter 7 Macroscopic Balances for Isothermal Flow Systems

4. Discuss the viscous loss E v and the compression term E c, with regard to physical interpreta-
tion, sign, and methods of estimation.
5. How is the macroscopic mechanical energy balance related to the Bernoulli equation for in-
viscid fluids? How is it derived?
6. What happens in Example 7.3-1 if one makes a different choice for the origin of the coordinate
system?
7. In Example 7.5-1 what would be the error in the final result if the estimation of the viscous
loss E v were off by a factor of 2? Under what circumstances would such an error be more seri-
ous?
8. In Example 7.5-1 what would happen if 5 ft were replaced by 50 ft?
9. In Example 7.6-3, how would the results be affected if the outlet pressure were 11 atm instead
ofl.latm?
10. List all the assumptions that are inherent in the equations given in Table 7.6-1.

PROBLEMS 7A.1 Pressure rise in a sudden enlargement (Fig. 7.6-1). An aqueous salt solution is flowing
3
through a sudden enlargement at a rate of 450 U.S. gal/min = 0.0384 m /s. The inside
diameter of the smaller pipe is 5 in. and that of the large pipe is 9 in. What is the pressure rise
3
in pounds per square inch if the density of the solution is 63 lb m/ft ? Is the flow in the smaller
pipe laminar or turbulent?
Answer: 0.056 psi = 386 N/m 2

7A.2 Pumping a hydrochloric acid solution (Fig. 7A.2). A dilute HC1 solution of constant density
3
and viscosity (p = 62.4 lb w/ft , /JL = 1 cp) is to be pumped from tank 1 to tank 2 with no overall
change in elevation. The pressures in the gas spaces of the two tanks are y>\ — \ atm and p 2 — 4
4
atm. The pipe radius is 2 in. and the Reynolds number is 7.11 X 10 . The average velocity in
the pipe is to be 2.30 ft/s. What power must be delivered by the pump?
Answer: 2.3 hp = 1.7 kW

Tankl Tank 2
-300 ft
•<
V\ Vi
Pump \ Fig. 7A.2. Pumping of a hydrochloric acid
Inside radius 2 •< solution.

7A.3 Compressible gas flow in a cylindrical pipe. Gaseous nitrogen is in isothermal turbulent
flow at 25°C through a straight length of horizontal pipe with 3-in. inside diameter at a rate of
0.28 lb m/s. The absolute pressures at the inlet and outlet are 2 atm and 1 atm, respectively.
Evaluate the viscous loss E v, assuming ideal gas behavior.
3
= 6.12 X 10 J/kg
Answer: 26.3 Btu/lb m
7A.4 Incompressible flow in an annulus. Water at 60°F is being delivered from a pump through a
coaxial annular conduit 20.3 ft long at a rate of 241 U.S. gal/min. The inner and outer radii of
the annular space are 3 in. and 7 in. The inlet is 5 ft lower than the outlet. Determine the
power output required from the pump. Use the mean hydraulic radius empiricism to solve
the problem. Assume that the pressures at the pump inlet and the annular outlet are the
same.
Answer: 0.31 hp = 0.23 kW