Problem 4: Water flows through a pipe whose internal diameter is 2.0 cm at a speed of 1.0 ms-1. What should be the diameter of the nozzle if water is to emerge at a speed of 4.0 ms-1.
Given Internal diameter = 2.0 cm => internal radius = r1 = 1.0 cm = 0.01 m
Speed of water in the pipe = v1 = 1.0 ms-1
Speed of efflux = v2 = 4.0 ms-1
Required Diameter of the nozzle =?
Formula Equation of continuity states
Where v1 is the velocity at cross-sectional area A1 and v2 is the velocity of water at cross-sectional area A2.
Now cross-sectional area is related to the radius as A = πr2. Therefore, cross-sectional area of the pipe
Cross-sectional area of the nozzle
Put all these values in the formula
Therefore, diameter of the nozzle should be