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,

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

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

At what height can the water rise in the water pipes of a multi-store house, if the ground water pressure is pp = 10^610^6 Pa. If the density of the water is ρ = 1 000 "kg/m"^3 ρ = 1 000 "kg/m"^3 ?