From a flow-net, which of the following information can be obtained?
A. Rate of flow
B. Pore water pressure
C. Exit gradient
D. Permeability
Choose the most appropriate answer from the options given below:
Step 1: Understanding flow-net.
A flow-net is a graphical representation of seepage through soils, consisting of flow lines and equipotential lines. It helps to analyze seepage problems without solving differential equations.
Step 2: Information that can be obtained.
- (A) Rate of flow: Yes, it can be determined using the number of flow channels and potential drops.
- (B) Pore water pressure: Yes, it can be estimated at any point using the equipotential lines.
- (C) Exit gradient: Yes, it can be computed using the slope of the hydraulic head near the downstream side.
- (D) Permeability: No, permeability is a soil property and must be determined through laboratory or field tests, not from a flow-net.
Step 3: Conclusion.
Thus, from a flow-net, we can obtain A, B, and C only.
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:
In a constant head permeameter, having cross-sectional area of $20 \, \text{cm}^2$, when the flow was taking place under a hydraulic gradient of $0.5$, the amount of water collected is $1200 \, \text{cm}^3$ in $60 \, \text{sec}$. The permeability of the soil is:
If the effective stress strength parameters are $C' = -10 \, \text{kPa}$ and $\phi' = 30^\circ$, the shear strength on a plane, within the saturated soil mass at a point where total normal stress is $300 \, \text{kPa}$ and pore water pressure is $150 \, \text{kPa}$, will be: