1. Equations of state provide the linkage between ___________ and ____________
a) Conservative, non-conservative equation
b) Eulerian, Lagrangian equations
c) Energy equation, mass and momentum equations
d) Differential, Integral equations
Explanation: Equations of the state provide the linkage of Energy equation with mass and momentum equations. They give the thermodynamic properties in terms of the state variables.
2. The principle of conservation is applicable to _______ systems.
a) isolated system
b) closed system
c) open system
d) all the systems irrespective of its type
Explanation: The principle of conservation is applicable only to the systems where there will not be any transfer of matter or energy. Isolated system will have these characters.
3. The fluid is subdivided into fluid parcels and every fluid parcel is followed as it moves through space and time. Which kind of formulation is this?
a) Cartesian
b) Eulerian
c) Lagrangian
d) Euclidian
Explanation: In Lagrangian fluid flow specification, the fluid is subdivided into many parts and each of this part is followed. These parts are called fluid parcels.
4. Each parcel in the Lagrangian formulation is tagged using __________
a) time-dependent position vector
b) time-independent position vector
c) time-dependent velocity vector
d) time-independent velocity vector
Explanation: The tag is time-independent so that the tag does not vary along with the flow. Position vector is chosen to follow the parcel along its position.
5. Which of these will best define positions of the parcel in increasing time?
a) Streamline
b) Streakline
c) Boundary line
d) Pathline
Explanation: Pathline is the one which represents the path of a fluid element along its way. So, to define the positions of the parcels, pathline is the best.
6. Which of these is an acceptable tag for Lagrangian parcels?
a) Parcel’s centre of mass at instantaneous time
b) Parcel’s centre of pressure at instantaneous time
c) Parcel’s centre of mass at initial time
d) Parcel’s centre of pressure at initial time
Explanation: Parcel’s centre of pressure is not suitable as it depends not only on position but on many variables too. Instantaneous time continuously varies along with the path. So, it cannot be a tag.
7. According to Eulerian approach, which of these is correct?
a) Both location and fluid move
b) Location moves and fluid is stationary
c) Both location and fluid are stationary
d) Location is stationary and fluid moves
Explanation: According to Eulerian approach, a particular location is chosen and the fluid flows past this location. This flowing fluid is analysed.
8. The independent variables in Eulerian approach are __________ and __________
a) instantaneous time and instantaneous position
b) initial time and instantaneous position
c) instantaneous time and Initial position
d) initial time and initial position
Explanation: Current position and time are the variables on which other variables depend on in Eulerian approach. These are the independent variables.
9. In Lagrangian approach, the flow parcels follow __________
a) pressure field
b) velocity field
c) temperature field
d) density field
Explanation: Velocity field defines the motion of fluid. Parcels also follow the same path of the fluid and therefore, parcels can be said to follow the velocity field.
10. Let,
t → Instantaneous time
\( \vec{v} \) → Velocity in x-direction
\( \vec{x} \) → Instantaneous position
\( \vec{x_0} \)→ Initial position
The relationship between Eulerian and Lagrangian approaches for velocity in x direction is given by _______
a) \( \vec{v}(t, \vec{x}(\vec{x_0}, t)) = \frac{\partial \vec{x} (\vec{x_0}, t)}{\partial t} \)
b) \( \vec{v}(t, \vec{x}(\vec{x_0}, t)) = \frac{\partial \vec{x_0} (\vec{x}, t)}{\partial t} \)
c) \( \vec{v}(t, \vec{x_0}(\vec{x}, t)) = \frac{\partial \vec{x} (\vec{x_0}, t)}{\partial t} \)
d) \( \vec{v}(t, \vec{x_0}(\vec{x}, t)) = \frac{\partial \vec{x_0} (\vec{x}, t)}{\partial t} \)
Explanation: Location at any instantaneous time is
\(\vec{x}(\vec{x_0}, t) \)
Velocity of fluid flow in Lagrangian approach is
\( \frac{\partial \vec{x}(\vec{x_0}, t)}{\partial t}\)
Velocity of fluid flow in Eulerian approach is
\( \vec{x}(t, \vec{x} (\vec{x_0}, t)) \)
The relationship between the approaches is
\(\vec{x}(t, \vec{x} (\vec{x_0}, t)) = \frac{\partial \vec{x}(\vec{x_0}, t)}{\partial t} \).