When friction and contraction of the water at the hole are taken into account, the model in Problem 11 becomes

dh/dt = -c A_h/A_w ˆš2gh,

where 0 < c < 1. How long will it take the tank in Problem 11(b) to empty if c = 0.6? See Problem 13 in Exercises 1.3.

Data from problem 13 (Exercise 1.3)

Suppose water is leaking from a tank through a circular hole of area Ah at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per secondto cA_hˆš2gh, where c (0 < c < 1) is an empirical constant. Determine a differential equation for the height h of water at time t for the cubical tank shown in the following figure. The radius of the hole is 2 in., and g ­= 32 ft/s².

Transcribed Image Text:

Aw 10 ft circular hole