Continuity Equation

When fluids move through a full pipe, the volume of fluid that enters the pipe must equal the volume of fluid that leaves the pipe, even if the diameter of the pipe changes. This is a restatement of the law of conservation of mass for fluids.

Problem 1 1. Water runs through a water main of cross-sectional area 0.4 m2 with a velocity of 6 m/s. Calculate the velocity of the water in the pipe when the pipe tapers down to a cross-sectional area of 0.3 m2.

Problem 2 2. Water enters a typical garden hose of diameter 1.6 cm with a velocity of 3 m/s. Calculate the exit velocity of water from the garden hose when a nozzle of diameter 0.5 cm is attached to the end of the hose.

First, find the cross-sectional areas of the entry (A1) and exit (A2) sides of the hose. Next, apply the continuity equation for fluids to solve for the water velocity as it exits the hose (v2).

Reference : http://www.aplusphysics.com/courses/honors/fluids/continuity.html