Question

Orange juice is being held in a tank before the bottling operation. The tank is filled to 4 m depth, has a 2.5 m diameter and is pressurized at 2 bar (gauge pressure). At the bottom of the tank there is discharge port that is 15 cm in diameter. (2 Points) Calculate the discharge velocity of the orange juice and (1 Point) the amount of time required to drain the tank, assuming the flow is steady and frictionless. Assume the density of the orange juice as 1050 kg/m3.

Answer 1

a)
pressure at the top point of the tank,

P1 = Po + 2*10^5 pa

v1 = 0

h1 = 4 m

pressure at the discharge port, P2 = Po

h2 = 0

v2 = ?

use Bernoulli's equation

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

P0 + 2*10^5 + 0 + rho*g*h1 = Po + (1/2)*rho*v2^2 + 0

(1/2)*rho*v2^2 = 2*10^5 + rho*g*h1

(1/2)*1050*v2^2 = 2*10^5 + 1050*9.8*4

v2 = sqrt((2*10^5 + 1050*9.8*4)/525)

= 21.4 m/s <<<<<<<<-----------Answer

b) volume flow rate, dV/dt

= A*v2

= (pi*0.15^2/4)*21.4

= 0.378 m^3/s

time taken to discharge the tanjk, t = Volume of the tank/(dv/dt)

= pi*R^2*h/(dV/dt)

= pi*1.25^2*4/0.378

= 52 s   <<<<<<<<-----------Answer