Question

Pipe $1$ has the radius and length of $0.2\text{m}$ and $50\text{m}$ respectively connected with the pipe $2$ having radius and length of $0.4\text{m}$ and $100\text{m}$ respectively. Find the total resistance offered to the flow of water by the system of pipes, Ignoring the resistance offered by the joint.
($\eta$ is the viscosity of water)

• A. $8.95\times {10}^4\eta$
• B. $5.5\times {10}^5\eta$
• C. $4.56\times {10}^5\eta$
• D. $2.86\times {10}^6\eta$

Answer 1

The correct option is A $8.95\times {10}^4\eta$

Given, radius of pipe $1$, $r_1=0.2\text{m}$
Length of pipe $1$, $l_1=50\text{m}$
Given, radius of pipe $2$, $r_2=0.4\text{m}$
Length of pipe $2$, $l_2=100\text{m}$
Both pipe $1$ and pipe $2$ are in series.
So, total resistnace offered to the flow is given by $R=R_1+R_2$
$R=\frac{8\eta l_1}{\pi r_1^4}+\frac{8\eta l_2}{\pi r_2^4}$ [where, $\eta$ = viscosity of water]
$\Rightarrow R=\frac{8\eta \times 50}{\pi \times (0.2{)}^4}+\frac{8\times \eta \times 100}{\pi \times (0.4{)}^4}=8.95\times {10}^4\eta$
$\Rightarrow R=8.95\times {10}^4\eta$