What gauge pressure is required in the city mains for a stream from a fire hose connected to the mains to reach a vertical height of 15 m? (Ans: 147 kPa)



Data Given:


Height  = h = 15 m

value of g = 9.8 m s⁻² 

Density of water = ⍴ = 1000 kg m⁻³


To Find:


Pressure difference (Pressure Gauge)  = P₁ - P₂ = ?


Solution:

We have find first he speed of water at fire house v₂ and taking the speed v₁ approximately to zero at the top.

So the Bernoulli's equation can be written as 


P₁   =  P₂ + `\frac {1}{2}`⍴v₂² 

or

P₁ - P₂  = `\frac {1}{2}`⍴v₂² 

Where the  speed v₂ is also unknown so by using Torricelli equation  v₂ = `\sqrt {2gh}` thus putting the value of v₂ in the above equation.

P₁ - P₂  = `\frac {1}{2}`⍴ (`\sqrt {2gh}`)² 

or

P₁ - P₂  = ⍴gh 


By putting values

P₁ - P₂  = 1000 kg m⁻³ ï½˜ 9.8 m s⁻² ï½˜15 m

P₁ - P₂  = 147,000 Pa

or

P₁ - P₂  = 147 kPa -----------------Ans.



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