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.
A fixed control volume has four one-dimensional boundary sections (1, 2, 3, and 4). For a steady flow inside the control volume, the flow properties at each section are tabulated below:
The rate of change of energy of the system which occupies the control volume at this instant is \( E \times 10^6 \, {J/s} \). The value of \( E \) (rounded off to 2 decimal places) is ........
A liquid flows under steady and incompressible flow conditions from station 1 to station 4 through pipe sections P, Q, R, and S as shown in the figure. Consider, \( d \), \( V \), and \( h \) represent the diameter, velocity, and head loss, respectively, in each pipe section with subscripts ‘P’, ‘Q’, ‘R’, and ‘S’. \( \Delta h \) represents the head difference between the inlet (station 1) and outlet (station 4). All the pipe sections are placed on the same horizontal plane for which the figure shows the top view.
(Insert diagram here, if possible)
Figure shows the steady and incompressible flow of a fluid in the direction of the arrow from section A to section D. Three pipe connectors are to be placed between sections at A and D having Total Energy Line (TEL) and Hydraulic Grade Line (HGL) as depicted in the figure. Consider, \( g \), \( P \), \( Q \), \( V \), \( \gamma \), and \( Z \) denote gravitational acceleration, pressure, volume flow rate, velocity, specific weight, and elevation of the centerline of the pipe connectors from the datum, respectively. Which one of the following options, in sequence, indicates the correct nature of connectors between sections A and B, B and C, and C and D in the direction of flow?
In the figures given below, L and H indicate low and high pressure centers, respectively; PGF, CoF and CeF indicate Pressure Gradient Force, Coriolis Force and Centrifugal Force, respectively; \( V \) is Velocity. [The arrows indicate only the directions but not the magnitudes of the forces and velocity.]
Which of the following is/are the correct representation(s) of the directions of various forces and velocity in the gradient wind balance in the northern hemisphere?
Which of the following is the correct form of the mass divergence form of the continuity equation for a compressible fluid? [In the given equations, \( \rho \) is the density and \( \nabla \) the three-dimensional velocity vector of the fluid.]
[(i)] $\displaystyle \frac{\partial \rho}{\partial t} + \nabla \times (\rho \mathbf{v}) = 0$
[(ii)] $\displaystyle \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0$
[(iii)] $\displaystyle \frac{\partial \mathbf{v}}{\partial t} + \rho \cdot \nabla \mathbf{v} = 0$
[(iv)] $\displaystyle \frac{\partial \rho}{\partial t} + \mathbf{v} \cdot \nabla \rho = 0$
The vertical (depth) profiles for three parameters P1, P2, and P3 in the northern Indian Ocean are given in the figure below. The values along the x-axis are the normalized values of the parameters and y-axis is the depth (m).
Identify the parameters P1, P2, and P3 from the options given below.