The ratio of the magnitudes of vorticity to rate of rotation in a fluid flow is ________.
Show Hint
- 2
- 3
- \( \frac{1}{2} \)
- 1
The Correct Option is A
Solution and Explanation
Step 1: Definition of Vorticity.
Vorticity is a measure of the local rotation of the fluid at a point, and it is defined as the curl of the velocity field: \[ \boldsymbol{\omega} = \nabla \times \mathbf{v}. \] Step 2: Definition of Rate of Rotation.
The rate of rotation in a fluid flow is the angular velocity of the fluid elements, which is proportional to the vorticity.
Step 3: Theoretical Relationship.
In some types of flows, the ratio of the magnitudes of vorticity to the rate of rotation is twice the rate of rotation, which is consistent with the behavior in certain types of fluid dynamics.
Step 4: Conclusion.
Thus, the ratio of the magnitudes of vorticity to rate of rotation is 2 in this case.
Correct Answer: (A) 2.
Top GATE NM Fluid Mechanics and Marine Hydrodynamics Questions
- The sum of the static pressure and dynamic pressure at a point in a fluid flow is called the ________.
- Identify the range of Reynolds number (Re) for a creeping flow.
- In a laminar boundary layer, the ratio of boundary layer thickness (\( \delta \)) to the corresponding displacement thickness (\( \delta^* \)) lies between ________.
- Which one of the following wave energy spectra is formulated for two peaks?
- According to linear water wave theory, at a point on the free surface of a regular wave, the phase difference between the free surface elevation and the horizontal water particle acceleration is ________.
Top GATE NM Fluid Mechanics Questions
- The sum of the static pressure and dynamic pressure at a point in a fluid flow is called the ________.
- Identify the range of Reynolds number (Re) for a creeping flow.
- In a laminar boundary layer, the ratio of boundary layer thickness (\( \delta \)) to the corresponding displacement thickness (\( \delta^* \)) lies between ________.
- For a freely floating body in water, which of the following degrees of freedom has/have inherent restoring force?
Match the non-dimensional numbers in Column 1 with the corresponding definitions in Column 2:
Top GATE NM Questions
- If \( \rightarrow \) denotes increasing order of intensity, then the meaning of the words [dry \( \rightarrow \) arid \( \rightarrow \) parched] is analogous to [diet \( \rightarrow \) fast \( \rightarrow \) \(\_\_\_\_\_\_\_\_\)]. Which one of the given options is appropriate to fill the blank?
- If two distinct non-zero real variables \( x \) and \( y \) are such that \( (x + y) \) is proportional to \( (x - y) \), then the value of \( \frac{x}{y} \) is:
- Consider the following sample of numbers: \[ 9, 18, 11, 14, 15, 17, 10, 69, 11, 13 \] The median of the sample is:
- The number of coins of ₹1, ₹5, and ₹10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in ₹5 coins is:
- For positive non-zero real variables \( p \) and \( q \), if \[ \log \left( p^2 + q^2 \right) = \log p + \log q + 2 \log 3, \] then the value of \( \frac{p^4 + q^4}{p^2 q^2} \) is: