MHT CET · Physics · Mechanical Properties of Fluids

When a liquid of density ' \(\rho\) ' flows through a tube of diameter ' \(d\) ' with critical velocity ' \(\mathrm{V}\) ' then the Reynolds number is
\(\text { ( } \eta=\text { coefficient of viscosity of liquid) }\)

A \(\frac{\eta \rho}{V d}\)
B \(\frac{\mathrm{Vd}}{\rho \eta}\)
C \(\frac{\mathrm{Vpd}}{\eta}\)
D \(\frac{V \eta d}{\eta}\)

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Answer & Solution

Correct Answer

(C) \(\frac{\mathrm{Vpd}}{\eta}\)

Step-by-step Solution

Detailed explanation

Dimensionless number that helps to find the dominant force between inertial force and viscous force. It is defined as,
\(\text { Reynold's number }=\frac{\text { inertial force }}{\text { viscous force }}=\left(\frac{\rho \mathrm{Vd}}{\eta}\right)\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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When a liquid of density ' \(\rho\) ' flows through a tube of diameter ' \(d\) ' with critical velocity ' \(\mathrm{V}\) ' then the Reynolds number is\(\text { ( } \eta=\text { coefficient of viscosity of liquid) }\)

Step-by-step Solution

When a liquid of density ' \(\rho\) ' flows through a tube of diameter ' \(d\) ' with critical velocity ' \(\mathrm{V}\) ' then the Reynolds number is
\(\text { ( } \eta=\text { coefficient of viscosity of liquid) }\)