Step 1: Recall definition of Reynolds number.
Reynolds number is:
\[
Re = \frac{\rho V L}{\mu} = \frac{\text{Inertia force}}{\text{Viscous force}}.
\]
Step 2: Check options.
- (1) Viscous/Inertia = Wrong (inverse of Reynolds).
- (2) Elastic/Pressure = Related to Mach number, not Reynolds.
- (3) Inertia/Viscous = Correct definition.
- (4) Gravity/Inertia = Related to Froude number, not Reynolds.
Step 3: Conclusion.
Hence, Reynolds number is the ratio of inertia force to viscous force.
The solution(s) of the ordinary differential equation $y'' + y = 0$, is:
(A) $\cos x$
(B) $\sin x$
(C) $1 + \cos x$
(D) $1 + \sin x$
Choose the most appropriate answer from the options given below:
For the matrix, $A = \begin{bmatrix} -4 & 0 \\ -1.6 & 4 \end{bmatrix}$, the eigenvalues ($\lambda$) and eigenvectors ($X$) respectively are:
The value of $\iint_S \vec{F} \cdot \vec{N} \, ds$ where $\vec{F} = 2x^2y \hat{i} - y^2 \hat{j} + 4xz^2 \hat{k}$ and $S$ is the closed surface of the region in the first octant bounded by the cylinder $y^2 + z^2 = 9$ and the planes $x = 0, x = 2, y = 0, z = 0$, is:
The value of the integral $\displaystyle \oint_C \frac{z^3 - 6}{2z - i} \, dz$, where $C: |z| \leq 1$, is:
Which of the following statements are true?
A. The same Bernoulli's equation is applicable to all the points in the flow field if the flow is irrotational.
B. The value of "Constant in the Bernoulli's equation" is different for different streamlines if the flow is rotational.
C. When a nozzle is fitted at the end of a long pipeline, the discharge increases.
D. The velocity of flow at the nozzle end is more than that in the case of a pipe without a nozzle, the head in both cases being the same.
Choose the most appropriate answer from the options given below: