Question
Water is flowing in a pipe of uneuqal cross-section at the place where the radius of the pipe is 1 cm whereas the velocity of water is 10 $cm / sec$. At any other place where the radius of the pipe is 2 cm then find the velocity of water.
✓
Answer
Given :
$ r_1=1 cm$
$
v_1=10 cm / sec
$
$r_2=2 cm$
Let velocity of water $\left( v _2\right)=$ ?
We know that
$\begin{aligned}A_1 v_1 & =A_2 v_2 \\
\pi r_1^2 v_1 & =\pi r_2^2 v_2 \\r_1^2 v_1 & =r_2^2 v_2 \\
(1)^2 \times 10 & =(2)^2 \times v_2 \\
10 & =4 V_2 \\
v_2 & =\frac{10}{4}=2.5 cm / sec\end{aligned}$
$ r_1=1 cm$
$
v_1=10 cm / sec
$
$r_2=2 cm$
Let velocity of water $\left( v _2\right)=$ ?
We know that
$\begin{aligned}A_1 v_1 & =A_2 v_2 \\
\pi r_1^2 v_1 & =\pi r_2^2 v_2 \\r_1^2 v_1 & =r_2^2 v_2 \\
(1)^2 \times 10 & =(2)^2 \times v_2 \\
10 & =4 V_2 \\
v_2 & =\frac{10}{4}=2.5 cm / sec\end{aligned}$
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