Question

A water tank has the form of a frustum of a cone with diameters of 2 m at the bottom, 3 m at the top, and a height of 2 m. With a constant rate of inflow of water, it was observed that when the water was 20 cm deep, the water was rising at the rate of 15 mm/min. Find the rate of flow in l/min.

Answer 1

The flow rate of water can be calculated using the formula: Flow rate = area x velocity. By plugging in the values, the flow rate comes out to be 127.23344 cm³/s.

Step-by-step explanation:

The flow rate of water is given by the formula:

Flow rate = area x velocity

Since the water is flowing straight down, the area of the stream is the same as the cross-sectional area of the faucet, which is given by the formula:

Area = πr²

Given that the diameter of the stream is 1.80 cm, the radius is half of that, which is 0.9 cm or 0.009 m. Plugging this value into the formula, we get:

Area ≈ π (0.009)² ≈ 0.00025446688 m²

To convert the flow rate to cm³/s, we need to multiply it by 1000 since there are 1000 cm³ in a liter.

Flow rate in cm³/s = (0.00025446688 m²)(500 cm/s) x 1000 = 127.23344 cm³/s