Power transmission in solid and hollow shaft

CASE 1:
WHEN THE OUTSIDE DIAMETER OF THE HOLLOW AND SOLID SHAFT IS SAME AND THEY ARE MADE OF SAME MATERIAL AND THE LENGTH AND THE ANGULAR VELOCITY WITH WHICH THEY ROTATE ARE THE SAME

CASE 2:
IF THE AREA OF CROSS SECTION OF BOTH THE HOLLOW AND THE SOLID SHAFT IS SAME ALONG WITH THE MATERIAL, LENGTH AND SAME ANGULAR VELOCITY

Before we start this case, have a look at these manipulations:

Weight = mass * g
              = density * volume * g
              = density * area * length * g

Out of weight, density, area and length, if any three of these are same for both solid and hollow shaft, fourth one has to be same.

So actually we stated each of these four parameters to be same in the heading, but even if three of them was given same, then the case would have been same still then.

IMPORTANT CONCLUSIONS:
• WHEN SPACE CONSTRAINT IS THERE THEN WE USE SOLID SHAFT FOR POWER TRANSMISSION AS WITH SAME EXTERNAL DIAMETER WE GET MORE TORQUE IN SOLID SHAFT.BUT ONE DISADVANTAGE IS THAT THE WEIGHT OF THE SHAFT WILL INCREASE.

• WHEN WE DON’T HAVE SPACE CONSTRAINTS THEN HOLLOW SHAFTS ARE BETTER CHOICE AS FOR THE SAME WEIGHT OF MATERIAL THEY TRANSMIT LARGER AMOUNT OF TORQUE.

• SAME APPLIES WITH THE STIFFNESS OF THE SHAFT WHICH IS BASICALLY TORQUE/ANGLE OF TWIST AND THE STIFFNESS VARIES ACCORDINGLY.

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