CHEMICAL ENGINEERING

22 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

end so that losses on entry and exit are negligible. One tank is 7 m diameter and contains
water to a depth of 7 m. The other tank is 5 m diameter and contains water to a depth of
3m.
If the tanks are connected to each other by means of the pipe, how long will it take
before the water level in the larger tank has fallen to 6 m? Assume the pipe to be of aged
mild steel.

Solution

The system is shown in Fig. 3a. If at any timetthe depth of water in the larger tank is
hand the depth in the smaller tank isH, a relationship betweenhandHmay be found.

Area of larger tankD/ 4  72 D 38 .48 m^2 ,

area of smaller tankD/ 4  52 D 19 .63 m^2.

7 m

dh

h

H x

5 m

5 m

7 m 300 m

75 mm bore

Figure 3a.

When the level in the large tank falls toh, the volume dischargedD 7 hð 38 .48 m^3.
The level in the small tank will rise by a heightx, given by:

xD 38. 48  7 h/ 19. 63 D 13. 72  1. 95 h

HDxC 3 D 16. 72  1. 95 h

The energy balance equation is:u^2 / 2 CgzCvP 1 P 2 DF

u^2 /2 may be neglected, andP 1 DP 2 Datmospheric pressure, so that:

gzDFDgzC 4 R/u^2 l/du^2 ,zDhHD 2. 95 h 16. 72 

or:  2. 95 h 16. 72 gD 4 R/u^2 l/du^2

and: uD

√

[ 2. 95 h 16. 72 g/ 4 R/u^2 l/d]

As the level falls fromhtohdhin time dt, the volume dischargedD 38. 48 dhm^3.

Hence: time,dtD

 38 .48 dh

/ 4  0. 075 ^2

√

[ 2. 95 h 16. 72 g/ 4 R/u^2 l/d]

or: dtD

2780 dh

√

[4R/u^2 l/d]

p

 2. 95 h 16. 72