Question

Water is poured into a bowl at a constant rate of 17.0 cm^3/s. The bowl has a circular cross section, but does not have a uniform diameter. (That is, different horizontal cross sections taken at different heights of the bowl have different diameters.) As the water fills the bowl, the water level reaches a point where the diameter of the bowl is
d1 = 1.45 cm.
What is the rate (in cm/s) at which the water level rises at this diameter?

Answer 1

Answer:

10.29 cm/s

Explanation:

Discharge in to the bowl = 17.0 cm³/s

Diameter of the bowl, d₁ = 1.45 cm

Now,

Rate at which water level rise at its diameter = $\frac{\textup{Discharge}}{\textup{Area of cross-section}}$

also,

Area of cross-section = $\frac{\pi}{\textup{4}}\times1.45^2$

or

Area of cross-section = 1.651 cm²

Therefore,

Rate at which water level rise at its diameter = $\frac{\textup{17}}{\textup{1.651}}$

or

Rate at which water level rise at its diameter = 10.29 cm/s