**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}.

**Solution**

**Given** Internal diameter = 2.0 cm => internal radius = r_{1} = 1.0 cm = 0.01 m

Speed of water in the pipe = v_{1} = 1.0 ms^{-1}

Speed of efflux = v_{2} = 4.0 ms^{-1}

**Required** Diameter of the nozzle =?

**Formula** Equation of continuity states

Where v_{1} is the velocity at cross-sectional area
A_{1} and v_{2} is the velocity of water at cross-sectional
area A_{2}.

Now cross-sectional area is related to the radius as A = πr^{2}.
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

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