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

`(Q_A)/(Q_B)=0.031`

Step-by-step 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=(8\mu LQ)/(\pi R^(4))`

`(L_AQ_A)/( R_A^(4))=(L_BQ_B)/( R_B^(4))`

`(Q_A)/(Q_B)=(R_A^4)/(R_B^4)* (L_B)/(L_A)`

`(Q_A)/(Q_B)=(r^4)/((2r)^4)* (L')/(2L')`

`(Q_A)/(Q_B)=(1)/(16)* (1)/(2)`

`(Q_A)/(Q_B)=0.031`