Statement of Reynolds Transport Theorem is given below with three blanks.
The rate of change of ............. extensive property can be calculated by summing the rate of change of the amount of same property in the ............. and the rate at which the property is ............. the surface of the control volume.
Which one of the following options correctly fills the blanks by using its comma-separated phrases in sequence?
The rate of change of ............. extensive property can be calculated by summing the rate of change of the amount of same property in the ............. and the rate at which the property is ............. the surface of the control volume.
Which one of the following options correctly fills the blanks by using its comma-separated phrases in sequence?
Show Hint
- system, control volume, exiting
- control volume, system, exiting
- system, control volume, entering
- control volume, control volume, entering
The Correct Option is A
Solution and Explanation
The Reynolds Transport Theorem (RTT) relates the rate of change of an extensive property within a control volume to the rate at which the property enters or exits the control volume. In the RTT, the property is first considered in the system and its total change is then analyzed as it flows in and out of the control volume.
Therefore, the correct sequence of phrases is:
- The rate of change of system extensive property can be calculated by summing the rate of change of the amount of the same property in the control volume, and the rate at which the property is exiting the surface of the control volume.
Thus, the correct answer is (A) system, control volume, exiting.
Top GATE XE Engineering Sciences Questions
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\[ \vec{V} = 5x\hat{i} - Py\hat{j} + 3k\hat{k} \] Here, \( \hat{i}, \hat{j}, \hat{k} \) are unit vectors along \( x, y, z \) directions, respectively and \( P \) is a constant.
Which one of the following options is the correct value of \( P \) that satisfies the conservation of mass for the given velocity field? - Conservation of mass for a steady axisymmetric flow field in the cylindrical \( (r, z) \) coordinates is:
\[ \frac{1}{r} \frac{\partial}{\partial r} (r V_r) + \frac{\partial V_z}{\partial z} = 0 \] Here, \( V_r \) and \( V_z \) are radial and axial components of velocity, respectively.
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Top GATE XE Fluid Mechanics Questions
- Fluid at a constant flow rate passes through a long, straight, cylindrical pipe that has an axisymmetric convergent section at the end.
Which one of the following options correctly represents the velocity field in the converging section in cylindrical \( (r, \theta, z) \) coordinates? - A sharp flat plate of length \( L \) and infinite width is immersed parallel to a fluid stream having velocity \( u_\infty \).
At a point on the plate, far away from the leading edge and not near the trailing edge, the boundary layer thickness, the displacement thickness, and the momentum thickness are denoted as \( \delta \), \( \delta^* \), and \( \theta \), respectively.
Which one of the following options correctly represents the relation between these thicknesses? Consider the following Statements [1] and [2].
Statement [1]: The Eulerian study focuses attention on individual particle and its motion is observed as a function of time.
Statement [2]: The Lagrangian study focuses attention on the motion of the particles passing through an identified point.
Which one of the following options identifies the correctness of the given statements?
- For a steady and incompressible flow, the velocity field \( \vec{V} \) in Cartesian \( (x, y, z) \) coordinate system is given as:
\[ \vec{V} = 5x\hat{i} - Py\hat{j} + 3k\hat{k} \] Here, \( \hat{i}, \hat{j}, \hat{k} \) are unit vectors along \( x, y, z \) directions, respectively and \( P \) is a constant.
Which one of the following options is the correct value of \( P \) that satisfies the conservation of mass for the given velocity field? - Conservation of mass for a steady axisymmetric flow field in the cylindrical \( (r, z) \) coordinates is:
\[ \frac{1}{r} \frac{\partial}{\partial r} (r V_r) + \frac{\partial V_z}{\partial z} = 0 \] Here, \( V_r \) and \( V_z \) are radial and axial components of velocity, respectively.
Which one of the following options is correct if \( \psi \) is the stream function?
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