A grinding wheel, used in a machine shop, dislodges many particles and projects
ID: 1464978 • Letter: A
Question
A grinding wheel, used in a machine shop, dislodges many particles and projects them from the contact point tangentially.
A particle of a certain size and density is projected 1 cm away (stopping distance S).
(a) (2 pts) How for will a particle of twice this size be projected?
(b) (2 pts) Estimate the projected distance of both particle sizes when the speed of the grinding wheel is doubled. Assume that the initial velocity of the particle is now twice.
(c) (2 pts) The stopping distance equation presented in class assumes that the particles are within the Stokes regime. Will the stopping distance be longer or shorter when doubling particle diameter for a Re > 1?
(d) (2 pts) Will the stopping distance be longer or shorter when doubling the initial velocity for the original particle for a Re > 1?
Explanation / Answer
The projected distance is propotional to the stopping distance,
S=v0t which is propotional to v0pdd2
S=stopping distance
V0=initial velocity
t=the time to reach 0.693 of the final velocity
The stopping distance depends on the square of the particle diameter, so for a particle that is two times larger will project four times the distance to 4cm
At twice the grinding wheel speed the particle will come off at approximately twice the initial velocity resulting in doubling the distance to 2 cm
The above stopping distance equation assumes that the particle in the stokes regime. If the particle velocity and the diameter are such that Rep is larger than 0.1, the stopping distance wil be somewhat less than quadrapoled for the larger particle.
This is because the drag increases faster with diameter outside the Stokes regime . Similiarly increasing the initial velocity also increases Rep and results somewhat less than doubling of the distance
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