(a) At what speed must the tank in Problem 5.9 be rotated for the center of the bottom to have zero depth of water?

(b) If the bottom circumferential plate is $\frac{1}{4}$ in thick, what is the stress in that plate?

Question

(a) At what speed must the tank in Problem 5.9 be rotated for the center of the bottom to have zero depth of water?

(b) If the bottom circumferential plate is [latex]\frac{1}{4} [/latex] in thick, what is the stress in that plate?

Accepted Answer

(a) Origin S will now be at point C in Fig. 5-7.

volume above liquid surface = volume of paraboloid

or [latex]\frac{1}{4}\pi 3^2 imes 1.50=\frac{1}{2}\pi x^2_{2}(6.00) [/latex] (1)

Also [latex]y_{2}=6.00=\frac{\omega ^2}{2 imes 32.2}x^2_{2} [/latex] (2)

From (1) and (2) we obtain [latex]\omega ^2 [/latex] = (12)(32.2)/1.125 = 343 and [latex]\omega [/latex] = 18.5 rad/sec.

(b) [latex]p^{′}_{D}=15.5+\frac{\gamma h}{144} [/latex] , where [latex]h=y_{1}=\frac{(18.5)^2(1.50)^2}{2 imes 32.2} =12.0 [/latex] ft

[latex]=15.5+\frac{62.4 imes 12.0}{144}=20.7 [/latex] psi . Stress at [latex]D=\sigma _{D}=\frac{p^{′}_{r}}{t}=\frac{20.7 imes 18}{\frac{1}{4} }=1490 [/latex]

Question 5.10: (a) At what speed must the tank in Problem 5.9 be rotated fo...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions