Question

Q.1) A large cylinder contains air a 102 kPa at a location where the surrounding air is at 100 kPa and -4 deg C. Now a 2 cm diameter hole is opened on the wall of the cylinder. Determine the maximum mass flow rate of air through the hole.

b.) is it reasonable to use the same method to solve this problem if the air pressure in the storage tank were 300 kPa? justify your answer with calculations.

Answer 1

Q1)

a) Use Beronulli's equation

P1 + (0.5)*rho*v1^2 = P2 + 0.5*rho*v2^2

P1 - P2 = 0.5*rho*(v2^2 - v1^2)

P1 - P2 = 0.5*rho*v2^2 (since v1 = 0)

v2 = sqrt(2*(P1-P2)/rho)

= sqrt(2*(102 - 100)*10^3/1.29)

= 55.7 m/s

volume flow rate = A2*v2

= (pi*0.02^2/4)*55.7

= 0.0175 m^3/s

mass flow rate = density*volume flow rate

= 1.29*0.0175

= 0.0226 kg/s

b)

simillarly,
sqrt(2*(P1-P2)/rho)

= sqrt(2*(300 - 100)*10^3/1.29)

= 557 m/s

volume flow rate = A2*v2

= (pi*0.02^2/4)*557

= 0.175 m^3/s

mass flow rate = density*volume flow rate

= 1.29*0.175

= 0.226 kg/s

It is not reasonable.

because air can not move with speed 557 m/s