Recent questions tagged numerical-answers

The Fourier cosine series of a function is given by : $$f\left ( x \right ) = \sum_{n = 0}^{\infty} f_{n} \cos nx$$ For $f\left ( x \right ) = \cos^{4} x$, the numerical ...

An uncompacted heap of soil has a volume of $10000\: m^{3}$ and void ratio of $1$. If the soil is compacted to a volume of $7500\: m^{3}$, then the corresponding void rat...

A weld is used for joining an angle section $\text{ISA}$ $100 \:mm \times 100\:mm \times 10 \:mm$ to a gusset plate of thickness $15$ $\text{mm}$ to transmit a tensile lo...

Consider the differential equation $$\frac{\mathrm{dy} }{\mathrm{d} x} = 4 \left ( x + 2 \right ) - y$$ For the initial condition $y = 3$ at $x = 1$, the value of $y$ at ...

A set of observations of independent variable $(x)$ and the corresponding dependent variable $(y)$ is given below.$$\begin{array}{|c|c|} \hline\text{x} & 5 & 2 & 4 & 3 \\...

The plane truss shown in the figure is subjected to an external force $P$. It is given that $P = 70\; kN$, $a = 2\; m$, and $b = 3\; m$.The magnitude (absolute value) of ...

Consider the linearly elastic plane frame shown in the figure. Members $\text{HF, FK and FG}$ are welded together at joint $F$. Joints $\text{K, G and H}$ are fixed suppo...

Consider a simply supported beam $\text{PQ}$ as shown in the figure. A truck having $100$ $\text{kN}$ on the front axle and $200$ $\text{kN}$ on the rear axle, moves from...

A reinforced concrete beam with rectangular cross section (width = $300$ $\text{mm}$, effective depth = $580$ $\text{mm}$) is made of $M30$ grade concrete. It has $1\%$ l...

A raft foundation of $30\:m \times 25\:m$ is proposed to be constructed at a depth of $8\:m$ in a sand layer. A $25\:m$ thick saturated clay layer exists $2 m$ below the ...

A two-hour duration storm event with uniform excess rainfall of $3\:cm$ occurred on a watershed. The ordinates of streamflow hydrograph resulting from this event are give...

Two reservoirs are connected by two parallel pipes of equal length and of diameters $20\:cm$ and $10\:cm$, as shown in the figure (not drawn to scale). When the differenc...

Depth of water flowing in a $3\:m$ wide rectangular channel is $2\:m$. The channel carries a discharge of $12\:m^{3}/s$. Take $g = 9.8\; m/s^{2}$.The bed width (in $m$) a...

A wastewater sample contains two nitrogen species, namely ammonia and nitrate. Consider the atomic weight of $\text{N, H, and O}$ as $14\:g/mol$, $1\:g/mol$, and $16\:g/m...

A two-phase signalized intersection is designed with a cycle time of $100\:s$. The amber and red times for each phase are $4\:s$ and $50\:s$, respectively. If the total l...

At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of $4$ vehicles per hour and $2$ vehicles per hour...

The vehicle count obtained in every $10$ minute interval of a traffic volume survey done in peak one hour is given below.$$\begin{array}{|c|c|} \hline \text{Time Interval...

For the dual-wheel carrying assembly shown in the figure, $P$ is the load on each wheel, $a$ is the radius of the contact area of the wheel, $s$ is the spacing between th...

The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________

A solid circular torsional member $\text{OPQ}$ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent materi...

A horizontal angle $\theta$ is measured by four different surveyors multiple times and the values reported are given below.$$\begin{array}{|lc|cI|cI|cI|cI|cI|}\hline&\tex...

A function is defined in Cartesian coordinate system as $f(x,y)=xe^{y}$. The value of the directional derivative of the function ($\textit{in integer}$) at the point $(2,...

An elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of $\text{1.5 m}$. It is supported on a solid steel circular column of diam...

A prismatic fixed-fixed beam, modelled with a total lumped-mass of $\text{10 kg}$ as a single degree of freedom $\text{(SDOF)}$ system is shown in the figure.If the flexu...

A fire hose nozzle directs a steady stream of water of velocity $\text{50 m/s}$ at an angle of $45^{\circ}$ above the horizontal. The stream rises initially but then even...

A rectangular cross-section of a reinforced concrete beam is shown in the figure. The diameter of each reinforcing bar is $\text{16 mm}$. The values of modulus of elastic...

The activity details for a small project are given in the Table.$$\begin{array}{|cl|cI|cI|}\hline&\textbf{Activity} & \textbf{Duration (days)} & \textbf{Depends on} \\ \h...

An equipment has been purchased at an initial cost of $₹ 160000$ and has an estimated salvage value of $₹ 10000$. The equipment has an estimated life of $5$ years. The di...

The soil profile at a road construction site is as shown in figure (not to scale). A large embankment is to be constructed at the site. The ground water table $\text{(GWT...