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 (`\frac {d₁}{2}`)²,

A₂ = π r₂² = π (`\frac {d₂}{2}`)²,

Putting values in equation (1)

 π (`\frac {d₁}{2}`)² v₁ = π (`\frac {d₂}{2}`)² v₂

or

d₁² v₁ = d₂² v₂

or

d₂² = d₁² `\frac {v₁}{v₂}`

or (taking square root bothside)

d₂ = d₁`\sqrt frac {v₁}{v₂}`

by putting values 

d₂ = 0.01 m ｘ`\sqrt frac {1 m s⁻¹}{21 m s⁻¹}`

d2 = 0.01 m ｘ `\sqrt {0.0476}`

d₂ = 0.01 m ｘ 0.2182

d₂ = 0.002182 m

or

d₂ = 0.2 cm---------------Ans.




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