The Equation Of Continuity

To determine the rate of flow, we will use the principle of conservation of mass and Bernoulli's equation. The problem involves a fluid with a known density flowing through a pipe that tapers to half its original cross-sectional area.

First, calculate the cross-sectional area of the narrow section:

Using the principle of conservation of mass, the rate of flow through both sections of the pipe is equal. Thus, we have the equation:

where is the fluid density, and and are the fluid velocities in the wide and narrow sections, respectively.

By canceling and solving for :

Next, apply Bernoulli's equation, which relates pressures, velocity, and height in fluid flow, assuming height difference is zero:

Substitute and rearrange to find :\)

The rate of flow is given by :\)

Converting to the desired unit:

Therefore, the rate of flow of the liquid is 2.4 × 10⁻³ m³ s⁻¹, which lies within the given range (24,24).