Dimensionless Numbers

Q. An airplane is cruising at a speed of 800 km/h at an altitude where the air temperature is $0^{\circ }C.$ The flight Mach number at this speed is nearly

1. 1.3
2. 0.67
3. 0.25
4. 2.4

Q. Match List-1 (Non-dimensional numbers) with List-2 (Application) and select the correct answer using the codes given below the lists:
List-1
A. Mach Number
B. Thoma Number
C. Reynolds Number
D. Weber Number

List-2
1. Waves in an ocean
2. Launching of rockets
3. Cavitation phenomenon
4. Capillary flow in soil
5. Motion of a submarine

1. A-1, B-3, C-5, D-2
2. A-3, B-2, C-4, D-1
3. A-2, B-3, C-5, D-4
4. A-2, B-1, C-3, D-4

Q. Euler number or pressure coefficient may be represented as (notations have their usual meanings)

1. $\frac{\Delta P}{\gamma H}$
2. $\frac{\Delta P}{\left(\rho V^2/2\right)}$
3. $\frac{\Delta P}{\mu V/L}$
4. $\frac{\Delta P}{\rho Lg}$

Q. Match List-1 with List-2 and select the correct answer using the codes given below the lists:
List-1
A. Froude number
B. Euler number
C. Reynolds number
D. Mach number

List-2
1. Related to inertia force and elastic force
2. Related to inertia force and viscous force
3. Related to inertia force and pressure force
4. Related to inertia force and gravity force

1. A-4, B-1, C-3, D-2
2. A-2, B-3, C-4, D-1
3. A-4, B-3, C-2, D-1
4. A-2, B-1, C-4, D-3

Q. Group-I Contains dimensionless parameter and
Group-II contains ratio

Group-I
P. Mach number
Q. Reynold number
R. Weber number
S. Froude number
Group-II
1. Ratio of inertial force and gravity force.
2. Ratio of fluid velocity and velocity of sound.
3. Ratio of inertial force and viscous force.
4. Ratio of inertial force and surface tension force.

Correct match of the dimensionless parameter in Group-I with Group-II is

P Q R S

1. $$\begin{array}{cccc}3& 2& 4& 1\end{array}$$
2. $$\begin{array}{cccc}3& 4& 2& 1\end{array}$$
3. $$\begin{array}{cccc}2& 3& 4& 1\end{array}$$
4. $$\begin{array}{cccc}1& 3& 2& 4\end{array}$$

Q.

Give the significance of the Reynolds number.

Q. There are four variables, namely, E (volume modulus of elasticity), p (pressure per unit area). g(acceleration due to gravity) and $\mu$ (viscosity of water). They are associated with Mach, Euler, Froude and Renylods number, respectively, in the order

1. E, p, $\mu$, g
2. p, E, $\mu$, g
3. p, E, g, $\mu$
4. E, p, g, $\mu$

Q. Match List-1 with List-2 and select the correct answer using the codes given below the lists:
List-1
A. Reynolds number
B. Froude number
C. Mach number
D. Weber number

List-2
1. Formation of liquid droplet
2. High speed flow of a gas
3. Flow in closed conduits
4. Sloping interface exists between fluids of different densities

1. A-3, B-4, C-2, D-1
2. A-2, B-1, C-3, D-4
3. A-3, B-1, C-2, D-4
4. A-2, B-4, C-3, D-1