Calculating Velocity of an Incompressible Liquid Flowing Through a Conduit

Explanation:

Principle of Continuity:

According to the principle of continuity, the flow rate (Q) of an incompressible fluid remains constant along a pipe of varying diameter. This means that the velocity of the fluid will change as the diameter of the conduit changes.

Calculating Velocity at Location 1:

At location 1, the diameter is 2.5 cm, which corresponds to a radius of 1.25 cm (0.0125 m). The cross-sectional area can be approximated as 0.00012272 m². Given the velocity of 2 m/s, we can calculate the flow rate at location 1 using the formula Q = (0.00012272 m²)(2 m/s) = 0.00024544 m³/s.

Calculating Velocity at Location 2:

At location 2, the diameter is 5 cm, resulting in a radius of 2.5 cm (0.025 m). By rearranging the formula Q = Av to solve for v, we get v = Q/A = 0.00024544 m³/s ÷ (π(0.025 m)²) ≈ 0.624 m/s. Therefore, the velocity at location 2 is approximately 0.624 m/s.