The force acting on the bottom of the cylinder of Example 2.12 is nearest:
A) 55.6 N
B) 50.4 N
C) 45.2 N
D) 38.4 N rpm. The highest pressure in the U-tube is nearest:

Question

Quizplus · Accepted Answer

$55.6 \mathrm {~N}$
The pressure distribution on the bottom of the cylinder, using $p = 0$ at $r = 0$, is (see Eq. 2.6.4)
$$p - 0 = \frac { \rho \omega ^ { 2 } } { 2 } \left( r ^ { 2 } - 0 \right) \quad \text { or } \quad p = \frac { 1000 } { 2 } 26.6 ^ { 2 } r ^ { 2 } = 353800 r ^ { 2 }$$
Integrate over the bottom area:
$$F _ { \text {bottom } } = \int _ { 0 } ^ { 0.1 } 353800 r ^ { 2 } \times 2 \pi r d r = 2 \pi \times \frac { 353800 \times 0.1 ^ { 4 } } { 4 } = \underline { 55.6 \mathrm {~N} }$$

The Force Acting on the Bottom of the Cylinder of Example