Water flows from a pipe at 650 L / min. (a) What is the diameter (in cm ) of the pipe if the ve

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Water flows from a pipe at 650 L / min. (a) What is the...

Water flows from a pipe at $650 \mathrm{~L} / \mathrm{min}$. (a) What is the diameter (in $\mathrm{cm}$ ) of the pipe if the velocity of the water is $1.5 \mathrm{~m} / \mathrm{s}$ ? (b) Find the velocity (in $\mathrm{m} / \mathrm{s}$ ) of the water if the diameter of the pipe is $20.0 \mathrm{~cm} .$

Key Concepts

Unit Conversion

Proper unit conversion is essential in fluid dynamics calculations to ensure consistency across equations. Converting units, such as transforming liters per minute to cubic meters per second or centimeters to meters, is necessary for accurate computations.

Cross-Sectional Area of a Circular Pipe

The cross-sectional area of a circle, given by A = ?(d/2)², is crucial in problems involving pipes. It allows for the computation of fluid velocity when combined with the volumetric flow rate and is a key element in applying the continuity equation.

Volumetric Flow Rate

Volumetric flow rate is the measure of the volume of fluid passing through a given cross-section per unit time. It connects to the continuity equation by the relation Q = A × v, where Q is the flow rate, A is the cross-sectional area, and v is the velocity of the fluid.

Continuity Equation

This principle in fluid dynamics states that for an incompressible fluid, the product of the cross-sectional area and the velocity of the fluid remains constant along a streamline. It is used to relate the velocity and diameter of a pipe when dealing with varying flow conditions.

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