What is the formula to calculate flow velocity given the flow rate and cross-sectional area?

The formula to calculate flow velocity is derived from the relationship between flow rate, cross-sectional area, and velocity. Flow rate (Q) is defined as the volume of fluid that passes through a cross-section per unit time. The relationship can be expressed with the formula:

[ Q = A \cdot v ]

where:

• ( Q ) is the flow rate,
• ( A ) is the cross-sectional area, and
• ( v ) is the flow velocity.

To find the flow velocity, you can rearrange this formula to solve for ( v ):

[ v = \frac{Q}{A} ]

This indicates that the flow velocity is directly proportional to the flow rate and inversely proportional to the cross-sectional area. If the flow rate increases, the velocity increases, provided the area remains constant. Conversely, if the area increases while keeping the flow rate constant, the flow velocity decreases.

This formula is essential for various applications in fluid mechanics, engineering, and environmental studies, allowing engineers to design systems that control or utilize fluid flow efficiently.

The other options presented do not accurately relate flow rate, area, and velocity according to the principles of fluid mechanics, which is why they do not represent the correct relationship.