Question

Determine the ratio of the flow rate through capillary tubes A and B (that is, QA/QB). The length of A is twice that of B, and the radius of A is one-half that of B. The pressure across both tubes is the same. Express your answer using three significant figures.

Answer 1

Answer:

$\dfrac{Q_A}{Q_B}=0.031$

Explanation:

Lets take

Radius of tube A=r

Length of tube A=L

Radius of tube B= r'

Length of tube B=L'

Given that

L = 2 L'

r= 0.5 r'

r' = 2 r

The pressure across tube given as

$\Delta p=\dfrac{8\mu LQ}{\pi R^{4}}$

$\dfrac{L_AQ_A}{ R_A^{4}}=\dfrac{L_BQ_B}{ R_B^{4}}$

$\dfrac{Q_A}{Q_B}=\dfrac{R_A^4}{R_B^4}\times \dfrac{L_B}{L_A}$

$\dfrac{Q_A}{Q_B}=\dfrac{r^4}{(2r)^4}\times \dfrac{L'}{2L'}$

$\dfrac{Q_A}{Q_B}=\dfrac{1}{16}\times \dfrac{1}{2}$

$\dfrac{Q_A}{Q_B}=0.031$