fine sand moves through pipes just like fluid. a sandblasting machine moves fine sand through a pipe of inner diameter 2.8 cm at 75L/minutes. the sand comes out from two identical jets at speed 45 m/s. calculated the diameter of the holes through which the jets come out.(answer is 4.21mm)

Answer 1

Use continuity equation, namely the volume of sand coming out per second equals the diameter * speed of sand.

Volume = 75 L/min = 1.25 L/s

Total area of jets (d=diam in dm)
=2π(d²)/4

Speed of sand = 45 m/s = 450 dm/s

Equate volumes of sand
450*2π(d²)/4=1.25
d=sqrt(1.25*4/(450*2π))
=0.04205 dm
=4.205 mm