Is my math correct?

posted by .

Find the Inside diameter(d) and outside diameter(D) of a hollow shaft given:
Power transmitted by shaft=1400kW
Shaft speed=45 RPM
Angle of twist on shaft=1 degree
Shaft lenght(L)=25D
Assume d=0.6D
Modulus of Rigidity(G)=81.75GPa

My answer:
Shaft ang. vel.=45*2pi/60s
A.V.=4.71rads/s
Torque transmitted by shaft=Power/A.V.
Torque=1400000W/4.71
T=297240Nm
Then using the Torsion equation:
T=297240
J=pi/32*(D^4-d^4)
G=81.75X10^9
Angle of twist=1*pi/360=0.01745
L=25D
Using the general torsion equation:
T/J=G*Twist ang./L
287240Nm/J=(81.75X10^9)*0.01745/25D
J=297240X25D/(81.75X10^9)*0.01745
J=0.005209D
Since J=pi/32*(D^4-d^4)
Then:
0.005209D=pi/32*(D^4-0.6D^4)
(0.005209D*32)/pi=1D^4-0.1296D^4
0.05307D=0.8704D^4
D^3=0.05307D/0.8704D
D^3=0.06097
D=39.35cm(ans.)
d=39.35*0.6=23.61cm(ans.)
Hope this is correct!
Thank you for checking it out.

  • Is my math correct? -

    The angular velocity is correct.
    The torque (T) is correct
    The angle of twist in radians is pi/180, not pi/360, but the 0.01745 rad is correct.
    The annulus polar moment of inertia (J) formula is correct.
    The stress/strain formula is correct.
    D has been calculated properly and cnverted to centimeters. I did not check all of the numbers, but all steps seem to have been followed correctly.

  • Is my math correct? -

    Thank you so much

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. applied mechanics

    A solid shaft of 65mm outside diameter and a hollow shaft of 85mm outside diameter are connected by 6 bolts with the mean pitch of thread being 155mm. The shear stress due to the torque on the shafts is equal to the shear stress on …
  2. Torque and shear stress

    A solid shaft of 65mm outside diameter and a hollow shaft of 85mm outside diameter are connected by 6 bolts with the mean pitch of thread being 155mm. The shear stress due to the torque on the shafts is equal to the shear stress on …
  3. physic

    A solid shaft of 65mm outside diameter and a hollow shaft of 85mm outside diameter are connected by 6 bolts with the mean pitch of thread being 155mm. The shear stress due to the torque on the shafts is equal to the shear stress on …
  4. Applied Mech.2

    Find the Inside diameter(d) and outside diameter(D) of a hollow shaft given: Power transmitted by shaft=1400kW Shaft speed=45 RPM Angle of twist on shaft=1 degree Shaft lenght(L)=25D Assume d=0.6D Modulus of Rigidity(G)=81.75GPa My …
  5. Physics

    A solid shaft of 65mm outside diameter and a hollow shaft of 85mm outside diameter are connected by 6 bolts with the mean pitch of thread being 155mm. The shear stress due to the torque on the shafts is equal to the shear stress on …
  6. applied mechanics

    A solid shaft of 65mm outside diameter and a hollow shaft of 85mm outside diameter are connected by 6 bolts with the mean pitch of thread being 155mm. The shear stress due to the torque on the shafts is equal to the shear stress on …
  7. physics

    A drive shaft of a belt conveyor system transmits 12kW of power at a speed of 40 rpm. If the shaft diameter is 50mm * 120mm long, calculate a)The shear stress in the shaft. b)The angle of twist if modulus of rigidity =80 GN/m2 c)If …
  8. algebra

    The horsepower (hp) that a shaft can safety transmit varies jointly with its speed (in revolutions per minute, or rpm) and the cube of the diameter. If a shaft of a certain material 2 in in diameter can transmit 36 hp at 75 rpm, what …
  9. Statics

    A solid, round simply supported steel shaft has a diameter of 25mm and span length of 500mm. The shaft supports a concentrated load of 3kN at midspan. Calculate the maximum deflection of the shaft.
  10. physics

    A hollow steel shaft has an external diameter of 120 mm and is 10 mm thick. It is coupled to a solid shaft of the same material, 100 mm in diameter. If the length of the hollow shaft is 960 mm, find the length of the solid shaft, so …

More Similar Questions