rotation

Problem 20 - Rotating Vessel

Problem
A closed cylindrical vessel 3 m. in diameter and 6 m high is filled with water to a height of 4.5 m. The rest is filled with air, the pressure of which is 105 kPa. If the vessel is rotated at 191 rpm about its axis, determine the maximum and minimum inside pressure at the base.
 

08-001-rotating-pressure-vessel.gif

 

Moment of a Force

Moment is the measure of the capacity or ability of the force to produce twisting or turning effect about an axis. This axis is perpendicular to the plane containing the line of action of the force. The magnitude of moment is equal to the product of the force and the perpendicular distance from the axis to the line of action of the force. The intersection of the plane and the axis is commonly called the moment center, and the perpendicular distance from the moment center to the line of action of the force is called moment arm.
 

52-53 Two cars traveling from the same point but going to different directions

Problem 52
A car drives south at 20 mi/hr. Another car, starting from the same point at the same time and traveling 40 mi/hr, goes east for 30 minutes then turns north. Find the rate of rotation of the line joining the cars (a) 1 hour after the start; (b) at the time the second car makes its turn.

49-51 Ship sailing east and turned N 30d E

Problem 49
A ship, moving 10 mi/hr, sails east for 2 hours, then turns N 30° E. A searchlight, placed at the starting point, follows the ship. Find how fast the light is rotating (a) 4 hours after the start; (b) just after the turn.

46-48 Rate of rotation of the searchlight

Problem 46
A ship, moving at 8 mi/hr, sails east for 2 hr, then turns N 30° W. A searchlight, placed at the starting point, follows the ship. Find how fast the light is rotating, (a) 3 hr after the start; (b) just after the turn.

Solution to Problem 322 Torsion

Problem 322
A solid steel shaft is loaded as shown in Fig. P-322. Using G = 83 GPa, determine the required diameter of the shaft if the shearing stress is limited to 60 MPa and the angle of rotation at the free end is not to exceed 4 deg.
 

Solution to Problem 140 Pressure Vessel

Problem 140
At what angular velocity will the stress of the rotating steel ring equal 150 MPa if its mean radius is 220 mm? The density of steel 7.85 Mg/m3.
 

Solution 140
140-fbd-rotating-ring.gif$CF = M \omega^2 \bar x$
 

Where:
$M = \rho V = \rho A \pi R$

$x = 2R / \pi$

 

Thus,
$CF = \rho A \pi R \omega^2 (2R / \pi)$

Solution to Problem 139 Pressure Vessel

Problem 139
Find the limiting peripheral velocity of a rotating steel ring if the allowable stress is 20 ksi and steel weighs 490 lb/ft3. At what revolutions per minute (rpm) will the stress reach 30 ksi if the mean radius is 10 in.?
 

 
 
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