Calculating Flow Speed in a Constriction
What is the flow speed in the constriction when a pipe narrows to 2.0-cm diameter?
How can we use the principle of continuity to determine the flow speed in the constriction?
Flow Speed Calculation:
When the pipe narrows to a 2.0-cm diameter, the flow speed in the constriction is approximately 5.28 cm/s.
To calculate the flow speed in the constriction, we can apply the principle of continuity, which states that the mass flow rate of an incompressible fluid remains constant in a closed system. This principle allows us to analyze how the flow speed changes as the pipe diameter varies.
Initially, when the water flows through a pipe with a diameter of 2.5cm, we can calculate the initial cross-sectional area using the formula: A = πr^2, where r is the radius (half the diameter). The initial cross-sectional area is found to be 4.91 cm2.
Given the initial flow speed of 1.9 m/s, we can determine the initial volume flow rate using the formula Q = A * v. Plugging in the values, we obtain an initial volume flow rate of 9.34 cm3/s.
When the water enters the constriction with a diameter of 1.5cm, we can calculate the cross-sectional area of the constriction to be 1.77 cm2. By rearranging the formula, v = Q / A, we find the flow speed in the constriction to be 5.28 cm/s.
Therefore, by applying the principle of continuity and using the formula for volume flow rate, we can determine the flow speed in a constriction when the pipe diameter changes.