A mixing beater consists of three thin rods, each 10.5 cm long. The rods diverge

Question

A mixing beater consists of three thin rods, each 10.5 cm long. The rods diverge from a central hub, separated from each other by 120°, and all turn in the same plane. A ball is attached to the end of each rod. Each ball has cross-sectional area 3.90 cm2 and is so shaped that it has a drag coefficient of 0.620. The drag force on each ball is R = 1/2*D**A*v2 where D is the drag coefficient,the density of the fluid, A the cross-sectional area, and v the speed of the object moving through the fluid.

(a) Calculate the power input required to spin the beater at 1000 rev/min in water.

Explanation / Answer

speed of the beater=1000 rev/min=1000*2*pi radians/min

=6283.2 radians/minute

=6283.2/60 radians/sec

=104.72 radians/sec

then linear speed=angular speed*radius

=104.72*0.105

=10.996 m/sec

then drag force on each ball=0.5*D*pho*A*v^2

=0.5*0.62*1000*3.9*10^(-4)*10.996^2

=14.618 N

then power required to drive each ball=force*veloicty=14.618*10.996=160.74 W

then power required to drive all the three balls=160.74*3=482.22 W

hence power input required is 482.22 W

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