Answer:
[tex]0.0168 m^3/s[/tex]
Explanation:
We are given that
[tex]r_1=0.0183 m[/tex]
[tex]h_1=0[/tex]
[tex]r_2=0.0420 m[/tex]
[tex]h_2=12.6 m[/tex]
Let [tex]P_1=P_2=P[/tex]
By using Bernoulli theorem
[tex]P+\frac{1}{2}\rho v^2_1+\rho gh_1=P+\frac{1}{2}\rho v^2_2+\rho gh_2[/tex]
[tex]\frac{1}{2}\rho v^2_1+\rho gh_1=\frac{1}{2}\rho v^2_2+\rho gh_2[/tex]
[tex]v^2_1+2gh_1=v^2_2+2gh_2[/tex]
[tex]A_1v_1=A_2v_2[/tex]
[tex]v_1=\frac{A_2v_2}{A_1}[/tex]
[tex](\frac{A_2}{A_1})^2v^2_2+2g\times 0=v^2_2+2\times 9.8\times 12.6[/tex]
[tex](\frac{\pi r^2_2}{\pi r^2_1})^2v^2_2-v^2_2=246.96[/tex]
[tex]v^2_2((\frac{r^2_2}{r^2_1})^2-1)=246.96[/tex]
[tex]v^2_2=246.96\frac{r^4_1}{r^2_4-r^4_1}[/tex]
[tex]v_2=\sqrt{246.96\frac{r^4_1}{r^4_2-r^4_1}}[/tex]
[tex]v_2=\sqrt{246.96\times \frac{(0.0183)^4}{(0.042)^4-(0.0183)^4}}[/tex]
[tex]v_2=3.038 m/s[/tex]
Volume flow rate =[tex]A_2v_2[/tex]
Volume flow rate =[tex]\pi r^2_2v_2=\pi (0.042)^2\times 3.038=0.0168 m^3/s[/tex]
