Page 209 - Bird R.B. Transport phenomena

Problems 193

7. Discuss the flow of water through a 1 /2-in. rubber garden hose that is attached to a house
faucet with a pressure of 70 psig available.
8. Why was Eq. 6.4-12 rewritten in the form of Eq. 6.4-13?
9. A baseball announcer says: "Because of the high humidity today, the baseball cannot go as far
through the heavy humid air as it would on a dry day/' Comment critically on this statement.

PROBLEMS

6A.1 Pressure drop required for a pipe with fittings. (a) Solve by Method A of Example 6.2-2.
What pressure drop is needed for pumping water at 20°C (b) Solve by Method В of Example 6.2-2.
through a pipe of 25 cm diameter and 1234 m length at a Answer: 4070 gal/hr
rate of 1.97 m/s? The pipe is at the same elevation through-
out and contains four standard radius 90° elbows and two 6A.4 Motion of a sphere in a liquid. A hollow sphere,
45° elbows. The resistance of a standard radius 90° elbow is 5.00 mm in diameter, with a mass of 0.0500 g, is released in
roughly equivalent to that offered by a pipe whose length a column of liquid and attains a terminal velocity of 0.500
3
is 82 diameters; a 45° elbow, 15 diameters. (An alternative cm/s. The liquid density is 0.900 g/cm . The local gravita-
2
method for calculating losses in fittings is given in §7.5.) tional acceleration is 980.7 cm/sec . The sphere is far
Answer: 4630 psi = 21.5 MPa enough from the containing walls so that their effect can
be neglected.
6A.2 Pressure difference required for flow in pipe with (a) Compute the drag force on the sphere in dynes.
elevation change (Fig. 6A.2). Water at 68°F is to be (b) Compute the friction factor.
pumped through 95 ft of standard 3-in. pipe (internal di-
ameter 3.068 in.) into an overhead reservoir. (c) Determine the viscosity of the liquid in centipoises.
(a) What pressure is required at the outlet of the pump to Answers: (a) 8.7 dynes; (b) / = 396; (c) 370 cp
6A.5 Sphere diameter for a given terminal velocity.
(a) Explain how to find the sphere diameter D corre-
45° elbow
sponding to given values of v^, p, p , fi, and g by mak-
s
ing a direct construction on Fig. 6.3-1.
(b) Rework Problem 2A.4 by using Fig. 6.3-1.
(c) Rework (b) when the gas velocity is 10 ft/s.
45° elbow
Pump \ 6A.6 Estimation of void fraction of a packed column.
A tube of 146 sq. in. cross section and 73 in. height is
packed with spherical particles of diameter 2 mm. When a
pressure difference of 158 psi is maintained across the col-
umn, a 60% aqueous sucrose solution at 20°C flows
through the bed at a rate of 244 lb/min. At this tempera-
Fig. 6A.2. Pipe flow system. ture, the viscosity of the solution is 56.5 cp and its density
3
is 1.2865 g/cm . What is the void fraction of the bed? Dis-
cuss the usefulness of this method of obtaining the void
supply water to the overhead reservoir at a rate of 18
gal/min? At 68°F the viscosity of water is 1.002 cp and the fraction.
density is 0.9982 g/ml. Answer: 0.30
(b) What percentage of the pressure drop is needed for 6A.7 Estimation of pressure drops in annular flow. For
overcoming the pipe friction? flow in an annulus formed by cylindrical surfaces of diam-
Answer: (a) 15.2 psig eters D and KD (with к < 1) the friction factors for laminar
and turbulent flow are
6A.3 Flow rate for a given pressure drop. How many
gal/hr of water at 68°F can be delivered through a 1320-ft Laminar (6А.7-1)
length of smooth 6.00-in. i.d. pipe under a pressure differ-
ence of 0.25 psi? Assume that the pipe is "hydraulically Turbulent A = G log (Re V?) - H (6A.7-2)
smooth/' 10 K