Question

Jon's bathtub is rectangular and its base is 18 ft2. How fast is the water level rising if Jon is filling the tub at a rate of 0.7 ft3/min?

Answer 1

To solve this problem we will use the concepts related to the volumetric flow rate, which describes the amount of volume per unit of time, through the Area of the section and the speed of the fluid over it. Mathematically this is:

$Q = A*V \rightarrow V = \frac{Q}{A}$

Where,

Q = Discharge

A= Cross sectional Area

V = Velocity

Our values are given as,

$A = 18ft^2$

$Q = 0.7ft^3/min$

Replacing,

$V = \frac{0.7}{18}$

$V = 0.038ft/min$

Therefore the water level rises to a velocity of 0.038ft/min