At what height can the water rise in the water pipes of a multi-store house, if the ground water pressure is #p# = #10^6# Pa. If the density of the water is # ρ = 1 000 "kg/m"^3 # ?

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Answer 1 · 2018-07-22T14:56:28

The height is #=91.8m#

Apply Bernouilli 's Equation

#p_1+1/2rhov_1^2+rhogh_1=p_2+1/2rhov_2^2+rhogh_2#

assume that the pipe's diameter does not change

#v_1=v_2#

Then,

#p_1+rhogh_1=p_2+rhogh_2#

The ground pressure #p_1=10^6Pa#

The atmospheric pressure is #p_2=10^5Pa#

The acceleration due to gravity is #g=9.8ms^-2#

The density of water is #rho=10^3kgm^-3#

Then

#10^6+rhogh_1=10^5+rhogh_2#

Then,

#rhog(h_2-h_1)=10^6-10^5#

#h_2-h_1=(9*10^5)/(10^3*9.8)=900/9.8=91.8m#