Page 245 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 225

d) If f remains almost constant, then show that the integration of Eq. (2) yields

Calculate the time required for h to drop from 4 m to 1.5 m.
e) Plot the variations of (4 and h as a function of time on the same plot. Show
that dhldt is negligible at all times in comparison with the liquid velocity through
the drain pipe system.
(Answer: c) 0.0039 d) 7.7min)

7.8 Consider draining of a spherical tank of diameter D with associated drain
piping as shown in the figure below. The tank is initially filled with water to an
elevation of H with respect to the reference plane.

a) Repeat the procedure given in Problem 7.7 and show that

where

x, = H* 3-R
X2=X;-R2
b) A spherical tank, 4m in diameter, discharges through a mild steel pipe system
(E = 4.6 x m) with an equivalent length of 100 m and a diameter of 23 cm.
Determine the time to drain the tank if H* = 1 m and H = 4.5 m.
(Answer: b) 4.9 min)