Water flows through a hose, whose internal diameter is 1 cm at a speed of 1 m s⁻¹. What should be the diameter of the nozzle if the water is to emerge at 21 m s⁻¹. (Ans: 0.2 cm)



Data Given:


Given:

Diameter of fire hose = d₁ = 1 cm = 0.01 m
Speed of water through hose = v₁ = 1 m s⁻¹
Speed of water through nozzle = v₂ = 21 m s⁻¹

To Find:

Diameter of nozzle = d₂ = ? 


Solution:

Using equation of  continuity

A₁v₁ = A₂v₂  -----------(1)

Where A₁ = π r₁² = π (d₁2)²,

A₂ = π r₂² = π (d₂2)²,

Putting values in equation (1)

 π (d₁2)² v₁ = π (d₂2)² v₂

or

d₁² v₁ = d₂² v₂

or

d₂² = d₁² v₁v₂

or (taking square root bothside)

d₂ = d₁√v₁v₂

by putting values 

d₂ = 0.01 m ｘ√1ms⁻¹21ms⁻¹

d2 = 0.01 m ｘ √0.0476

d₂ = 0.01 m ｘ 0.2182

d₂ = 0.002182 m

or

d₂ = 0.2 cm---------------Ans.




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