Question:
Two capillary tubes A and B are connected in series. The length and radius of the bore of tube A are twice those of tube B. The ratio of the pressure difference across the tubes A and B is:
Two capillary tubes A and B are connected in series. The length and radius of the bore of tube A are twice those of tube B. The ratio of the pressure difference across the tubes A and B is:
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In viscous flow, pressure drop depends strongly on radius: \( \Delta P \propto \frac{1}{r^4} \), so small radius change drastically affects flow.
Updated On: Jul 18, 2026
- 8:1
- 1:8
- 4:1
- 1:4
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The Correct Option is B
Solution and Explanation
Step 1: Poiseuille’s law basis.
\[ \Delta P \propto \frac{L}{r^4} \]
Step 2: Relation of tube A and B.
\[ L_A = 2L,\quad r_A = 2r \]
Step 3: Pressure drop in A.
\[ \Delta P_A \propto \frac{2L}{(2r)^4} = \frac{1}{8} \]
Step 4: Pressure drop in B.
\[ \Delta P_B \propto 1 \]
Step 5: Ratio.
\[ \Delta P_A : \Delta P_B = 1:8 \]
Step 6: Final conclusion.
\[ \boxed{1:8} \]
\[ \Delta P \propto \frac{L}{r^4} \]
Step 2: Relation of tube A and B.
\[ L_A = 2L,\quad r_A = 2r \]
Step 3: Pressure drop in A.
\[ \Delta P_A \propto \frac{2L}{(2r)^4} = \frac{1}{8} \]
Step 4: Pressure drop in B.
\[ \Delta P_B \propto 1 \]
Step 5: Ratio.
\[ \Delta P_A : \Delta P_B = 1:8 \]
Step 6: Final conclusion.
\[ \boxed{1:8} \]
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