Dimensionless Number MCQ Quiz in বাংলা - Objective Question with Answer for Dimensionless Number - বিনামূল্যে ডাউনলোড করুন [PDF]
Last updated on Mar 19, 2025
Latest Dimensionless Number MCQ Objective Questions
Top Dimensionless Number MCQ Objective Questions
Dimensionless Number Question 1:
Euler's number is the ratio of
Answer (Detailed Solution Below)
Dimensionless Number Question 1 Detailed Solution
Explanation:
Euler’s Number is defined as the square root of the ratio of the inertia force of a flowing fluid to the pressure force. Mathematically
Euler number \( = \sqrt {\frac{{Inertia\;force}}{{Pressure\;force}}}= \frac{V}{{\sqrt {P/\rho } }}\)
Other important dimensionless numbers are described in the table below:
|
Reynold’s number |
\(R_e=\frac{{{inertia force}}}{{{viscous force}}} = \frac{{{\bf{\rho VL}}\;}}{{\bf{\mu }}}\) |
|
Froude Number |
\({F_r} = \sqrt {\frac{{inertia\;force}}{{gravitation\;force}}} = \frac{V}{{\sqrt {{\bf{Lg}}} }}\) |
|
Mach Number |
\({M} = \sqrt {\frac{{inertia\;force}}{{Elastic\;force}}} = \frac{V}{{\sqrt {K/\rho } }}=~\frac VC \) |
|
Weber Number |
\({W_e} = \sqrt {\frac{{inertia\;force}}{{surface\;tension}}} = \frac{V}{{\sqrt {\sigma /\rho L} }}\) |
Dimensionless Number Question 2:
The only possible dimensionless group that combines velocity ‘V’, body size ‘L’, fluid density ‘ρ’ & surface tension ‘σ’
Answer (Detailed Solution Below)
Dimensionless Number Question 2 Detailed Solution
Explanation:
Dimensionless group:
- The group which has no dimension is called the dimensionless group.
- It is unitless.
| Quantity | Dimensional formula |
| Velocity (V) | LT-1 |
| Length (L) | L |
| Density (ρ) | ML-3 |
| Surface tension (σ) | MT-2 |
Dimensional formula of \(\frac {\rho L V^2}{\sigma}=\frac {ML^{-3} LL^2 T^{-2}}{MT^{-2}}= 0\)
Hence ,\(\frac {\rho L V^2}{\sigma}\) is a dimensionless group.
Dimensionless Number Question 3:
When the Mach number is more than 6, the flow is called
Answer (Detailed Solution Below)
Dimensionless Number Question 3 Detailed Solution
Explanation:
Mach number
- Mach number is defined as the ratio of inertia force to elastic force.
\(M = \sqrt {\frac{{Inertia\;force}}{{Elastic\;force}}} = \sqrt {\frac{{\rho A{V^2}}}{{KA}}} = \sqrt {\frac{{{V^2}}}{{\frac{K}{\rho }}}} = \frac{V}{{\sqrt {\frac{K}{\rho }} }} = \frac{V}{C}\;\;\;\;\left\{ {\sqrt {\frac{K}{\rho }} = C = Velocity\;of\;sound} \right\}\)
\(M = \frac{{velocity\;of\;body\;moving\;in\;fluid}}{{velocity\;of\;sound\;in\;fluid}}\)
For the compressible fluid flow, Mach number is an important dimensionless parameter. On the basis of the Mach number, the flow is defined.
|
Mach Number |
Type of flow |
|
M < 0.8 |
Sub-sonic flow |
|
0.8 < M <1.3 |
Trans-sonic |
|
M = 1 |
Sonic flow |
|
1 < M < 5 |
Super-sonic flow |
|
M > 5 |
Hypersonic flow |
Other important dimensionless numbers are described in the table below
|
Reynold’s number |
\(R_e=\frac{{{inertia force}}}{{{viscous force}}} = \frac{{{\bf{\rho VL}}\;}}{{\bf{\mu }}}\) |
|
Froude Number |
\({F_r} = \sqrt {\frac{{inertia\;force}}{{gravitation\;force}}} = \frac{V}{{\sqrt {{\bf{Lg}}} }}\) |
|
Euler number |
\({E_u} = \sqrt {\frac{{inertia\;force}}{{pressure\;force}}} = \frac{V}{{\sqrt {P/\rho } }}\) |
|
Weber Number |
\({W_e} = \sqrt {\frac{{inertia\;force}}{{surface\;tension}}} = \frac{V}{{\sqrt {\sigma /\rho L} }}\) |
Dimensionless Number Question 4:
Euler number is defined as the ratio of inertia forces to
Answer (Detailed Solution Below)
Dimensionless Number Question 4 Detailed Solution
Explanation:
Euler’s Number is defined as the square root of the ratio of the inertia force of a flowing fluid to the pressure force. Mathematically
Euler number \( = \sqrt {\frac{{Inertia\;force}}{{Pressure\;force}}}= \frac{V}{{\sqrt {P/\rho } }}\)
Other important dimensionless numbers are described in the table below:
|
Reynold’s number |
\(R_e=\frac{{{inertia force}}}{{{viscous force}}} = \frac{{{\bf{\rho VL}}\;}}{{\bf{\mu }}}\) |
|
Froude Number |
\({F_r} = \sqrt {\frac{{inertia\;force}}{{gravitation\;force}}} = \frac{V}{{\sqrt {{\bf{Lg}}} }}\) |
|
Mach Number |
\({M} = \sqrt {\frac{{inertia\;force}}{{Elastic\;force}}} = \frac{V}{{\sqrt {K/\rho } }}=~\frac VC \) |
|
Weber Number |
\({W_e} = \sqrt {\frac{{inertia\;force}}{{surface\;tension}}} = \frac{V}{{\sqrt {\sigma /\rho L} }}\) |
Dimensionless Number Question 5:
The Reynolds number which is used to predict whether the flow will be laminar or turbulent, is inversely proportional to
Answer (Detailed Solution Below)
Dimensionless Number Question 5 Detailed Solution
Explanation:
Reynolds Number
- Reynold number is a dimensionless number that helps to predict flow patterns in different fluid flow situations.
\({\rm{Re}} = \frac{{{\rm{Inertia\;force}}}}{{{\rm{Viscous\;force}}}} = {\rm{\;}}\frac{{{\rm{\rho V}}{{\rm{L}}_{\rm{c}}}}}{{\rm{\mu }}} = \frac{{{\rm{V}}{{\rm{L}}_{\rm{c}}}}}{{\rm{\nu }}}\)
Where,
Re = Reynolds number, ρ = density, V = velocity of flow
μ = dynamic viscosity ν = kinematic viscosity, LC = characteristic linear dimension
For pipe flow:
LC = diameter of pipe = D
Reynold number = \(Re = \frac{{{\rm{\rho VD}}}}{\mu } = \frac{{{\rm{VD}}}}{\nu }\)
- Laminar flow Re ≤ 2000
- Transition flow 2000 ≤ Re ≤ 4000
- Turbulent flow Re ≥ 4000
Dimensionless Number Question 6:
Dynamic similarity exists when the model and the prototype have the same:
Answer (Detailed Solution Below)
Dimensionless Number Question 6 Detailed Solution
Explanation:
Similitude
- The similitude is defined as the similarity between the model and its prototype in every aspect.
- It means that the model and prototype have similar properties or model and prototype are completely similar.
Three types of similarities must exist between model and prototype.
- Geometric similarity: the geometric similarity is said to exist between the model and prototype if the ratio of all corresponding linear dimensions in the model and prototype are equal.
\(\frac{{{L_p}}}{{{L_m}}} = \frac{{{D_p}}}{{{D_m}}} = {L_r}\)
where Lr is the scale ratio.
- Kinematic similarity: the kinematic similarity is said to exist between the model and prototype if the ratios of velocity and acceleration at the corresponding points in the model and the corresponding points in the prototype are the same.
\(\frac{{{V_p}}}{{{V_m}}} = {V_r}\)
where Vr is the velocity ratio.
\(\frac{{{a_p}}}{{{a_m}}} = {a_r}\)
where ar is the acceleration ratio.
Note: Direction of velocities in the model and the prototype should also be the same.
- Dynamic similarity: the dynamic similarity is said to exist between the model and prototype if the ratios of corresponding forces acting at the corresponding points are equal.
Also, the direction of corresponding forces at the corresponding points should be the same.
\(\frac{{{{\left( {{F_i}} \right)}_p}}}{{{{\left( {{F_i}} \right)}_m}}} = \frac{{{{\left( {{F_v}} \right)}_p}}}{{{{\left( {{F_v}} \right)}_m}}} = \frac{{{{\left( {{F_g}} \right)}_p}}}{{{{\left( {{F_g}} \right)}_m}}} \ldots = {F_r}\)
where Fr is the force ratio.
Dimensionless Number Question 7:
Which number has no effect surrounding fluid on fully submerged body?
Answer (Detailed Solution Below)
Dimensionless Number Question 7 Detailed Solution
Explanation:
Various Dimensionless numbers and their applications are given below.
|
Number |
Definition |
Significance |
|
Reynolds No |
\(Re = \frac{{Inertia\;Force}}{{Viscous\;Force}} \Rightarrow \frac{{\rho VL}}{\mu }\) |
Flow in closed conduit i.e. flows through pipes. |
|
Froude No |
\(Fr = \sqrt {\frac{{Inertia\;Force}}{{Gravity\;Force}}} \Rightarrow \frac{V}{{\sqrt {gL} }}\) |
Where a free surface is present and gravity force is predominant. Spillway, Open Channels, waves in the ocean. |
|
Euler No. |
\({E_u} = \sqrt {\frac{{Inertia\;Force}}{{Pressure\;Force}}} \Rightarrow \frac{V}{{\sqrt {\frac{p}{\rho }} }}\) |
In cavitation studies, where pressure force is predominant. |
|
Mach No. |
\(M = \sqrt {\frac{{Inertia\;Force}}{{Elastic\;Force}}} \Rightarrow \frac{V}{C}\) |
Where fluid compressibility is important. Launching of rockets, airplanes, and projectiles moving at supersonic speed. |
|
Weber No. |
\({W_e} = \sqrt {\frac{{Inertia\;Force}}{{Surface\;tension\;Force}}} \Rightarrow \frac{V}{{\sqrt {\frac{\sigma }{{\rho L}}} }}\) |
In Capillary studies i.e. where Surface tension is predominant. |
The square root, of the ratio of inertia force to gravity force, is called Froud Number
\(Fr = \sqrt {\frac{{Inertia\;Force}}{{Gravity\;Force}}} \Rightarrow \frac{V}{{\sqrt {gL} }}\)
Froude’s number has no effect surrounding fluid on a fully submerged body.
Dimensionless Number Question 8:
The dimensionless number defined by the ratio of inertial force to viscous force is called
Answer (Detailed Solution Below)
Dimensionless Number Question 8 Detailed Solution
Explanation:
Reynolds number:
- It is a dimensionless number that determines the nature of the flow of liquid through a pipe/plate etc.
- It is defined as the ratio of the inertial force to the viscous force for a flowing fluid.
- Reynold's number is written as Re.
\({Re} = \frac{{{\rm{Inertial\;force}}}}{{{\rm{Viscous\;force}}}}\)
Reynolds number plays a vital role in the analysis of fluid flow,
In Pipe flow:
- If Reynold's number lies between 0 - 2000, then the flow of liquid is streamlined or laminar.
- If Reynold's number lies between 2000 - 4000, the flow of liquid is unstable and changes from streamline to turbulent flow.
- If Reynold's number is above 4000, the flow of liquid is turbulent.
|
Number |
Definition |
Significance |
|
Reynolds No |
\(Re = \frac{{Inertia\;Force}}{{Viscous\;Force}} \Rightarrow \frac{{\rho VL}}{\mu }\) |
Flow in closed conduit i.e. flows through pipes. |
|
Froude No |
\(Fr = \sqrt {\frac{{Inertia\;Force}}{{Gravity\;Force}}} \Rightarrow \frac{V}{{\sqrt {gL} }}\) |
Where a free surface is present and gravity force is predominant. Spillway, Open Channels, waves in the ocean. |
|
Euler No. |
\({E_u} = \sqrt {\frac{{Inertia\;Force}}{{Pressure\;Force}}} \Rightarrow \frac{V}{{\sqrt {\frac{p}{\rho }} }}\) |
In cavitation studies, where pressure force is predominant. |
|
Mach No. |
\(M = \sqrt {\frac{{Inertia\;Force}}{{Elastic\;Force}}} \Rightarrow \frac{V}{C}\) |
Where fluid compressibility is important. Launching of rockets, airplanes, and projectile moving at supersonic speed. |
|
Weber No. |
\({W_e} = \sqrt {\frac{{Inertia\;Force}}{{Surface\;tension\;Force}}} \Rightarrow \frac{V}{{\sqrt {\frac{\sigma }{{\rho L}}} }}\) |
In Capillary studies i.e. where Surface tension is predominant. |
Dimensionless Number Question 9:
Reynolds number is significant in _____.
Answer (Detailed Solution Below)
Dimensionless Number Question 9 Detailed Solution
Reynold’s number is defined as the ratio of inertia force of the flowing fluid to the viscous force of the flowing fluid.
At low Reynold’s number, the viscous force dominates over the inertia force and the fluid flow with low velocity and in a streamlined manner and at high Reynold’s number, the inertia force dominates over the viscous force and at very high Reynolds number the fluid moves in random manner and intermixing takes place.
\(Re=\frac{\rho VD}{\mu }\) for pipe flow and \(Re=\frac{\rho Vx}{\mu }\) for flow over a plate.
Reynolds number is used in pipe flow, a duct flow, an open channel flow, flow resistance experienced by the submarines, airplanes, fully immersed body, flow through turbomachines at low speed, etc.
Dimensionless Number Question 10:
An oil having kinematic viscosity 1.5 × 10-4 m2/s is flowing through a pipe of 30 mm diameter. For the velocity of oil flow 25 m/s, the Reynold's number is
Answer (Detailed Solution Below)
Dimensionless Number Question 10 Detailed Solution
Concept:
Reynolds number signifies the ratio of inertia force to viscous force in velocity boundary layer. i.e. \(Re=\frac{F_i}{F_v}\)
Reynolds number also represents where the boundary layer changes from laminar to turbulent.
It is given in terms of viscosity:
\(Re=\frac{{\rho V L_c}}{\mu}=\frac{{ V L_c}}{ν}\)
where, ρ = density of fluid, V = velocity of fluid, L = characteristics length, μ = dynamic viscosity of fluid and ν = kinematic viscosity.
Characteristic length \(L_c=\frac{4A}{P}\)
For a pipe characteristic length is equal to the diameter.
Calculation:
Given:
d = 30 mm = 0.03 m, v = 1.5 × 10-4 m2/s, V = 25 m/s
Reynolds number:
\(Re=\frac{{ V L_c}}{ν}=\frac{{ VD}}{ν}\)
\(Re=\frac{{ 25\;\times\;0.03}}{1.5\;\times\;10^{-4}}=5000\)