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Determine the horse power (hp) transmitted at 1800 rpm by a shaft with diameter, d =1.306 if the torsional shear stress is limited to 8000 psi.
The strings:
S7P3A32 (Force - Push).
The math:
Pj Problem of Interest is of type force (push). work and power problems are of type force.
Torsional Shear Stress results from twisting.
Assumptions: sectional area of shaft is circular.
Neutral axis (line of zero stress) is located on the center line of the shaft.
Polar moment of inertia is a property of the shape of the section.
Equations of Interest:
Torsional shear stress, τ = (TD)/J ----------(1)
Where T = torque or twisting moment applied to section (lb in)
D = distance from neutral axis to outermost edges of section (inches)
J = Polar moment of inertia = (πd4)/32, for circular section (in4).
T = [63,000(hp)]/n ----------(2)
Where hp = horse power
n = revolution per min (rpm)
So, from equation (1);
Torsional shear stress, τ = (TD)/J
So, 8000 = [T(d/2)]/(πd4)/32
So, T = 3500 lb in.
So, From equation (2):
T = [63,000(hp)]/n
So, hp = (1800)(3500)/63000 = 100 hp.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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