1. Which method is used exclusively in fluid mechanics?
a) Lagrangian method
b) Eulerian method
c) Both Lagrangian and Eulerian methods
d) Neither Lagrangian nor Eulerian method
Explanation: In Fluid Mechanics, the matter of concern is the general state of motion at various points in the fluid system (as in Eulerian approach) rather than the motion of each particle (as in Lagrangian approach). Hence, the Eulerian method is extensively used in Fluid Mechanics
2. What type of flow can be taken for granted in a pipe of a uniform cross-section?
a) steady
b) unsteady
c) uniform
d) non-uniform
Explanation: According to the continuity equation, ρAV =constant, where ρ= density, A= cross-sectional area of flow, V = velocity of flow. For a pipe of a uniform cross-section, no matter what the rate of flow is, the velocity of flow inside the pipe will always remain constant. Hence, it’ll always be a uniform flow. It’ll be a steady flow if and only if the water level is maintained at a constant level by supplying water at the same rate as it gets discharged, else the water level will keep decreasing with time leading to an unsteady flow.
3. Can the flow inside a nozzle be steady and uniform?
a) yes
b) never
c) it can be steady but never uniform
d) it can be uniform but never steady
Explanation: According to the continuity equation, ρAV =constant, where ρ= density, A= cross-sectional area of flow, V = velocity of flow. For a nozzle, the area gradually decreases towards it’s exit. Thus, no matter what the rate of flow is, the velocity of flow at the nozzle exit will always be greater than that at it’s entrance. Hence, it’ll always be an unsteady flow. It can be a steady flow if and only if the water level is maintained at a constant level by supplying water at the same rate as it gets discharged, else the water level will keep decreasing with time leading to an unsteady flow.
4. Which of the following statements is true regarding one and two-dimensional flows?
a) Flow in a pipe is always taken as one-dimensional flow
b) Flow in a pipe is always taken as two-dimensional flow
c) Flow in a pipe is taken as one-dimensional flow when average flow parameters are considered
d) Flow in a pipe is taken as two-dimensional flow when average flow parameters are considered
Explanation: The flow inside a pipe can be described by the cylindrical co-ordinate system (r; θ; z), where r is in the radial direction, θ in the angular direction and z in the axial direction. For a circular cross-sections, the flow can be taken to be independent of θ. Hence, it can be taken aa a two-dimensional flow. Again if aerage flow parameters are considered to account for the variation in the radial direction, the flow can be taken as an one-dimensional flow.
5.Which of the following is true?
a) Flow is rotational inside the boundary layer and irrotational outside
b) Flow is irrotational inside the boundary layer and rotational outside
c) Flow is rotational both inside and outside of the boundary layer
d) Flow is irrotational both inside and outside of the boundary layer
Explanation: When a torque is applied to a fluid particle, it undergoes a rotation. Thus, the rotation of a fluid particle will alwayds be associated with shear stress. Shear stress is in turn dependent on the viscosity. Hence, rotational flow occurs where the viscosity effects are predominant. Since, viscosity effects are predominant inside the blundary layer, the flow will be rotational in this region. However, outside the boundary layer, the viscosity effects are negligible. Hence, flow can be treated as irrotational outside the boundary layer
6. Which of the following is true?
a) Flow is laminar inside the boundary layer and turbulent outside
b) Flow is turbulent inside the boundary layer and laminar outside
c) Flow is laminar both inside and outside of the boundary layer
d) Flow is turbulent both inside and outside of the boundary layer
Explanation: Flows can be characterized as laminar or turbulent on the basis of Reynold’s number Re = ρvd / μ, where ρ is the density, d is the pipe diameter and μ is the viscosity. For Re < 2000, the flow will be laminar and Re > 4000, the ow will be turbulent. For laminar flow, the viscosity effects must be high (μ should be high) as inside the boundary layer. Outside the boundary layer, the viscosity effects are negligible. Hence, the flow will be turbulent.
7.Three flows named as 1,2 and 3 are observed. The Reynold’s number for the three are 100, 1000 and 10000. Which of the flows will be laminar?
a) only 1
b) only 1 and 2
c) 1, 2 and 3
d) only 3
Explanation: Flows can be characterized as laminar or turbulent on the basis of Reynold’s number Re = ρvd / μ, where ρ is the density, d is the pipe diameter and μ is the viscosity. For Re < 2000, the flow will be laminar and Re > 4000, the flow will be turbulent. Thus, flow 1 and 2 will be laminar.
8. Three flows named as 1,2 and 3 are observed. The flow velocities are v1 and v2. If all other geometrical factors remain the same along with the fluid considered, flow is more likely to be laminar?
a) flow 1 if v1 > v2
b) flow 2 if v1 > v2
c) always flow 1
d) always flow 2
Explanation: Flows can be characterized as laminar or turbulent on the basis of Reynold’s number Re = ρvd / μ, where ρ is the density, d is the pipe diameter and μ is the viscosity. If all other geometrical factors remain the same along with the fluid considered, v1 > v2 implies Re1 > Re2. Thus, flow 2 is more likely to be laminar
9.What will be the shape of the pathline for an one-dimensional flow be like?
a) straight line
b) parabolic
c) hyperbolic
d) elliptical
Explanation: A pathline is the path followed by a particle in motion. For an one-dimensional flow, the fluids move in only one dimension (say x). Hence the pathline will also be a straight line (along that direction).
10. Which of the following is correct?
a) Pathlines of two particles in an one-dimensional flow can never intersect
b) Pathlines of two particles in an one-dimensional flow can never intersect if the two particles move along the same direction
c) Pathlines of two particles in an one-dimensional flow can intersect only if the two particles move along the same direction
d) Pathlines of two particles in an one-dimensional flow can intersect only if the two particles move along different directions
Explanation: The pathline of a particle in an one-dimensional flow is a straight line along the direction it moves. If the two particles move along the same direction, their pathlines will be parallel to each other and will never intersect.