Question 178: Properties of Matter

Question

Two tubes of radii r1  and r2, and lengths l1 and l2 , respectively, are connected in series
and a liquid flows through each of them in stream line conditions. P1  and P2  are pressure differences across the two tubes. 
If P2  is 4P1  and l2
 is $${{{1_1}} \over 4}$$, then the radius r2 will be equal to :

Accepted Answer

We know,
Rate of flow of liquid through  narrow tube,
$${{dv} \over {dt}}$$ = $${{\pi {{\Pr }^4}} \over {8\eta l}}$$
Both tubes  are connected in series  so rate of flow of liquid is same.
$$	herefore\,\,\,$$ $${{\pi {P_1}r_1^4} \over {8\eta {l_1}}}$$ = $${{\pi {P_2}r_2^4} \over {8\eta {l_2}}}$$
$$ \Rightarrow $$$$\,\,\,$$ $${{{P_1}{r_1}^4} \over {{l_1}}}$$ = $${{{P_2}{r_2}^4} \over {{l_2}}}$$
Given,
P
2
= 4P
1
and   $${l_2}$$ = $${{{l_1}} \over 4}$$
$$ \Rightarrow $$$$\,\,\,$$ $${{{P_1}{r_1}^4} \over {{l_1}}}$$ = $${{4{P_1}{r_2}^4} \over {{{{l_1}} \over 4}}}$$
$$ \Rightarrow $$$$\,\,\,$$ $${r_2}^4$$ = $${{{r_1}^4} \over {16}}$$
$$ \Rightarrow $$$$\,\,\,$$ r
2
= $${{{r_1}} \over 2}$$

Answer

r1

Answer

2r1

Answer

4r1

Answer

$${{{r_1}} \over 2}$$

Properties of Matter

Two tubes of radii r1 and r2, and lengths l1 and l2 , respectively, are connected in series and a liquid flows through each of them in stream line conditions. P1 and P2 are pressure differences across the two tubes. If P2 is 4P1 and l2 is ${{{1_1}} \over 4}$, then the radius r2 will be equal to :

Choose the correct answer: