Recent questions tagged numerical-answers

In a triaxial unconsolidated undrained $\text{(UU)}$ test on a saturated clay sample, the cell pressure was $100 \; \text{kPa}.$ If the deviatoric stress at failure was $...

A flood control structure having an expected life of $n$ years is designed by considering a flood of return period $T$ years. When $T = n,$ and $n \rightarrow \infty,$ th...

An undamped spring-mass system with mass $m$ and spring stiffness $k$ is shown in the figure. The natural frequency and natural period of this system are $\omega \; \text...

For the square steel beam cross-section shown in the figure, the shape factor about $z – z$ axis is $S$ and the plastic moment capacity is $M_{p}.$ Consider yield stress ...

A post-tensioned concrete member of span $15 \; \text(m)$ and cross-section of $450 \; \text{mm} \times 450 \; \text{mm}$ is prestressed with three steel tendons, each of...

A $100 \; \text{mg}$ of $\text{HNO}_{3}$ (strong acid) is added to water, bringing the final volume to $1.0 \; \text{liter}.$ Consider the atomic weights of $\text{H, N,}...

In a city, the chemical formula of biodegradable fraction of municipal solid waste $\text{(MSW)}$ is $\text{C}_{100} \text{H}_{250} \text{O}_{80} \text{N}.$ The waste has...

The concentrations $s(x,t)$ of pollutants in a one-dimensional reservoir at position $x$ and time $t$ satisfies the diffusion equation$$\frac{\partial s (x,t)}{\partial t...

A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals $4$ in exactly two of the three attempts is _______. (round of...

Consider two linear elastic rods $HI$ and $IJ$, each of length $b$, as shown in the figure. The rods are co-linear, and confined between two fixed supports at $H$ and $J....

The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams $UV$ and $WX$ are connected with the hel...

A uniform rod $KJ$ of weight $w$ shown in the figure rests against a frictionless vertical wall at the point $K$ and a rough horizontal surface at point $J.$ It is given ...

The activities of a project are given in the following table along with their durations and dependency.$$ \begin{array} {|c|c|c|} \hline \textbf{Activities}& \textbf{Dura...

A group of total $16$ piles are arranged in a square grid format. The center-to-center spacing $(s)$ between adjacent piles is $3 \; \text{m}.$ The diameter $(d)$ and len...

A saturated compressible clay layer of thickness $h$ is sandwiched between two sand layers, as shown in the figure. Initially, the total vertical stress and pore water pr...

A hydraulic jump takes place in a $6 \; \text{m}$ wide rectangular channel at a point where the upstream depth is $0.5 \; \text{m}$ (just before the jump). If the dischar...

A pump with an efficiency of $80\%$ is used to draw groundwater from a well for irrigating a flat field of area $108$ hectares. The base period and delta for paddy crop o...

Two discrete spherical particles ($\text{P}$ and $\text{Q}$) of equal mass density are independently released in water. Particle $\text{P}$ and particle $\text{Q}$ have d...

At a municipal waste handling facility, $30$ metric ton mixture of food waste, yard waste, and paper waste was available. The moisture content of this mixture was found t...

A sewage treatment plant receives sewage at a flow rate of $5000 \; \text{m}^{3}\text{/day}.$ The total suspended solids $\text{(TSS)}$ concentration in the sewage at the...

A sample of air analyzed at $25 \; ^{\circ}\text{C}$ and $1 \; \text{atm}$ pressure is reported to contain $0.04 \; \text{ppm}$ of $\text{SO}_{2}.$ Atomic mass of $\text{...

Assuming that traffic on a highway obeys the Greenshields model, the speed of a shockwave between two traffic streams $\text{(P)}$ and $\text{(Q)}$ as shown in the schema...

It is given that an aggregate mix has $260 \; \text{grams}$ of coarse aggregates and $240 \; \text{grams}$ of fine aggregates. The specific gravities of the coarse and fi...

Consider the following expression: $$z = \sin \left ( y + it \right ) + \cos \left ( y - it \right )$$ where $\text{z, y}$ and $t$ are variables, and $i = \sqrt{-1}$ is a...

The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be $30.0\text{ MPa}$. The value of maximum shear stress at this point is$7...

Four different soils are classified as $\text{CH, ML, SP, and SW}$, as per the Unified Soil Classification System. Which one of the following options correctly represents...

With respect to fluid flow, match the following in Column $X$ with Column $Y$:$$\begin{array}{|l|l|} \hline \qquad \textbf{Column X} & \qquad \textbf{Column Y} \\ \hline...

The total hardness in raw water is $500$ milligram per liter as $CaCO_{3}$. The total hardness of this raw water, expressed in milligram equivalent per liter, is(Consider...

An aerial photograph is taken from a flight at a height of $3.5$ $\text{km}$ above mean sea level, using a camera of focal length $152$ $\text{mm}$. If the average ground...

A line between stations $P$ and $Q$ laid on a slope of $1$ in $5$ was measured as $350\; m$ using a $50\; m$ tape. The tape is known to be shortly by $0.1\; m$.The correc...

Consider the following recursive iteration scheme for different values of variable $P$ with the initial guess $x_{1} =1$: $$x_{n + 1} = \frac{1}{2}\left ( x_{n} + \frac{P...

A concentrated vertical load of $3000$ $\text{kN}$ is applied on a horizontal ground surface. Points $P$ and $Q$ are at depths $1 \:m$ and $2\: m$ below the ground, respe...

At a site, Static Cone Penetration Test was carried out. The measured point (tip) resistance $q_{c}$ was $1000$ $\text{kPa}$ at a certain depth. The friction ratio $(f_{r...

During a particular stage of the growth of a crop, the consumptive use of water is $2.8$ $\text{mm}$/day. The amount of water available in the soil is $50\%$ of the maxim...

The bearing of a survey line is $N31 ^{\circ} 17’W$. Its azimuth observed from north is _________________ deg. (round off to two decimal places)