Question:easy
A glass tube of uniform cross-section is connected to a tap with a rubber tube. The tap is opened slowly. Initially the flow of water in the tube is streamline. The speed of flow of water to convert it into a turbulent flow is [radius of tube = $1\text{ cm}$, $\eta = 1 \times 10^{-3}\text{ Ns/m}^2$, $R_n = 2500$ and density of water = $10^3\text{ kg/m}^3$]
A glass tube of uniform cross-section is connected to a tap with a rubber tube. The tap is opened slowly. Initially the flow of water in the tube is streamline. The speed of flow of water to convert it into a turbulent flow is [radius of tube = $1\text{ cm}$, $\eta = 1 \times 10^{-3}\text{ Ns/m}^2$, $R_n = 2500$ and density of water = $10^3\text{ kg/m}^3$]
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Always double-check whether the parameter provided is radius or diameter. A very frequent pitfall is directly inserting $r$ instead of $d = 2r$ into the denominator of the Reynold equation, which incorrectly doubles the calculated velocity.
Updated On: Jun 11, 2026
- $0.15\text{ m/s}$
- $0.125\text{ m/s}$
- $0.3\text{ m/s}$
- $0.2\text{ m/s}$
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The Correct Option is B
Solution and Explanation
Step 1: Identify the controlling dimensionless group.
The streamline-to-turbulent switch is governed by the Reynolds number $R_n = \dfrac{\rho v d}{\eta}$. We simply set $R_n$ to its critical value and solve for the speed $v$.
Step 2: Rearrange for speed.
$v_c = \dfrac{R_n\,\eta}{\rho\,d}$.
Step 3: Convert the geometry.
Radius $r = 1\,\text{cm} = 10^{-2}\,\text{m}$, so the diameter is $d = 2r = 2 \times 10^{-2}\,\text{m}$.
Step 4: Insert the numbers.
$v_c = \dfrac{2500 \times (1 \times 10^{-3})}{(10^{3}) \times (2 \times 10^{-2})}$.
Step 5: Simplify top and bottom.
Numerator $= 2.5$; denominator $= 10^{3} \times 2 \times 10^{-2} = 20$. So $v_c = \dfrac{2.5}{20}$.
Step 6: Final value.
$v_c = 0.125\,\text{m/s}$, the speed at which the flow turns turbulent. \[ \boxed{v_c = 0.125\ \text{m/s}} \]
The streamline-to-turbulent switch is governed by the Reynolds number $R_n = \dfrac{\rho v d}{\eta}$. We simply set $R_n$ to its critical value and solve for the speed $v$.
Step 2: Rearrange for speed.
$v_c = \dfrac{R_n\,\eta}{\rho\,d}$.
Step 3: Convert the geometry.
Radius $r = 1\,\text{cm} = 10^{-2}\,\text{m}$, so the diameter is $d = 2r = 2 \times 10^{-2}\,\text{m}$.
Step 4: Insert the numbers.
$v_c = \dfrac{2500 \times (1 \times 10^{-3})}{(10^{3}) \times (2 \times 10^{-2})}$.
Step 5: Simplify top and bottom.
Numerator $= 2.5$; denominator $= 10^{3} \times 2 \times 10^{-2} = 20$. So $v_c = \dfrac{2.5}{20}$.
Step 6: Final value.
$v_c = 0.125\,\text{m/s}$, the speed at which the flow turns turbulent. \[ \boxed{v_c = 0.125\ \text{m/s}} \]
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