Asked by jay
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)
Answers
Answered by
MathMate
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
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
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