Question

A fountain designed to spray a column of water 7 m into the air has a 2 cm diameter nozzle at ground level. The water pump is 2 m below the ground. The pipe to the nozzle has a diameter of 4 cm. Assume laminar non-viscous flow. What is the necessary absolute pressure the pump must exert?

kpa

Answer 1

let r1 = 2 cm
h = 2 m
r2 = 4 cm

H = 7 m
P1 = 1 atm = 1.013*10^5 pa
P2 = ?

speed of the water from nozzle, v1 = sqrt(2*g*H)

= sqrt(2*9.8*7)

= 11.7 m/s

let v2 is the speed of the water from pipe.

use Continuty equation

A2*v2 = A1*v1

pi*r2^2*v2 = pi*r1^2*v1

v2 = v1*(r1/r2)^2

= 11.7*(2/4)^2

= 2.925 m/s

now use Bernoullie's equation

P2 + rhog*h2 + (1/2)*rho*v2^2 = P1 + rhog*h1 + (1/2)*rho*v1^2

P2 = P1 + rho*g*(h1-h2) + (1/2)*rho*(v1^2 - v2^2)

= 1.013*10^5 + 1000*9.8*2 + (1/2)*1000*(11.7^2 - 2.925^2)

= 1.85*10^5 pa

= 185 kPa <<<<<<<<--------------------Answer