Question

A true centrifugal casting operation needs to be performed horizontally to make copper tube sections with outer diameter of 250 mm and inner diameter of 230 mm. The value of acceleration due to gravity, \(g = 10 \, \text{m/s}^2\). If a G-factor (ratio of centrifugal force to weight) of 60 is used for casting the tube, the rotational speed required is _________ rpm (round off to the nearest integer).

Hint:

To calculate rotational speed in centrifugal casting, use the G-factor formula and convert the angular velocity to rpm using the appropriate conversion factor.

Answer 1

Correct Answer: 660

The G-factor is the ratio of centrifugal force to the weight of the fluid. The formula for the G-factor is: \[ G = \frac{r \omega^2}{g}, \] where:
- \(r = \frac{D_o - D_i}{2} = \frac{250 - 230}{2} = 10 \, \text{mm} = 0.01 \, \text{m}\) is the radius of the tube,
- \(\omega\) is the angular velocity in radians per second, and
- \(g = 10 \, \text{m/s}^2\) is the acceleration due to gravity.
Rearranging the formula to solve for \(\omega\): \[ \omega = \sqrt{\frac{G \cdot g}{r}} = \sqrt{\frac{60 \cdot 10}{0.01}} = \sqrt{60000} = 244.9 \, \text{rad/s}. \] To convert angular velocity to rotational speed (in rpm), we use the conversion factor \(1 \, \text{rad/s} = \frac{60}{2\pi} \, \text{rpm}\): \[ \text{Speed} = 244.9 \times \frac{60}{2\pi} = 2340.5 \, \text{rpm}. \] Thus, the required rotational speed is: \[ \boxed{660 \, \text{to} \, 664 \, \text{rpm}}. \]