A capillary tube of length L and radius r is connected with another...

Problems of series and parallel combination of pipes can be solved in the similar manner as is done in case of an electrical circuit. The only difference is potential difference is replaced by $\Delta p$ and electrical resistance as, $R_1=\frac{8 \eta L}{\pi r^4}=R and \quad R_2=\frac{8 \eta L}{\pi\left(\frac{r}{2}\right)^4}=16 R$ Electric current is replaced by rate of volume flow $V^{\prime}$. $\Rightarrow \quad$$\begin{aligned} p & =V R_1=V R....(i) \\ p^{\prime} & =p=V^{\prime} R_{\text{eq }}=V^{\prime}\left(R_1+R_2\right)=V^{\prime}(R+16 R) \\ & =17 V^{\prime} R\end{aligned}$$$...(ii) From Eqs. (i) and (ii), we get$$\begin{aligned} V R & =17 V^{\prime} R \\ \Rightarrow \quad V^{\prime} & =\frac{V}{17}\end{aligned}$$