Shaunti’s cola can is 20 cm tall and has a diameter of 5 cm. It is sitting on a

Question

Shaunti’s cola can is 20 cm tall and has a diameter of 5 cm. It is sitting on a brick wall 2 m above the ground.
When an unnamed individual shoots a BB hole 1 cm from the bottom of the can, Shaunti must initially place her
cola mug 79 cm from base of the wall in order to catch the stream of liquid. If the radius of the hole that was shot
in the can is 0.05 cm, what is the downward flow rate of cola in the can (in cm3 per minute)? (Assume the can is
full and that the density of coke is 1000 kg/m3)

Explanation / Answer

here diameter of can is large compared to that of the hole. the pressure at the top surface of can and at the hole is equal to atmospheric pressure   P1 = P2          the Bernoullis equation becomes                     (1/2) v12 + g y1 = g y 2                             v1 = ( 2g ( y2 - y1 ) ) 1/2   height of can   h1 = 20 cm = 0.2m height of brick wall   h2 = 2 m cola mug is placed 79 cm from the base of the wall            there fore    y 2   = 2+0.2 - 0.79   m                                    = 1.41 m   BB hole is 1 cm from the bottom of the can                        y 1 =   0.01 +2 -0.79                               = 1.22 m    velocity of a cola flowing out of a hole at the bottom of the can is                        v1 = ( 2*9.8 ( 1.41 - 1.22 ) ) 1/2                              = 1.9297 m/s     volume flow rate   Q = v 1 A                                       = 1.9297 * (0.05*10-2 ) 2                                         = 1.5*10-6 m3 / s                                        = 1.5*10-6 (102 cm ) 3( 60 )/ 60s                                        = 90 cm3 / m                                         = 1.9297 m/s     volume flow rate   Q = v 1 A                                       = 1.9297 * (0.05*10-2 ) 2                                         = 1.5*10-6 m3 / s                                        = 1.5*10-6 (102 cm ) 3( 60 )/ 60s                                        = 90 cm3 / m

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