Recent questions tagged numerical-answers

A hydraulically efficient trapezoidal channel section has a uniform flow depth of $2$ m. The bed width (expressed in m) of the channel is ______

Effluent from an industry ‘A’ has a pH of $4.2$. The effluent from another industry ‘B’ has double the hydroxyl (OH) ion concentration than the effluent from industry ‘A’...

While traveling along and against the traffic stream, a moving observer measured the relative flows as $50$ vehicles/hr and $200$ vehicles/hr, respectively. The average s...

The vertical angles subtended by the top of a tower T at two instrument stations set up at P and Q, are shown in the figure. The two stations are in line with the tower a...

Consider the following partial differential equation:$$3 \frac{\partial ^2 \phi}{ \partial x^2} + B \frac{ \partial ^2 \phi}{\partial x \partial y} + 3 \frac{\partial ^2 ...

$\underset{x \to 0}{\lim} \bigg( \dfrac{\tan x}{x^2-x} \bigg)$ is equal to _________

A $3 \: m$ thick clay layer is subjected to an initial uniform pore pressure of $145 \: kPa$ as shown in the figure.For the given ground conditions, the time (in days, ro...

A triangular pipe network is shown in the figure.The head loss in each pipe is given by $h_f = rQ^{1.8}$, with the variables expressed in a consistent set of units. The v...

The ordinates of a $2$-hour unit hydrograph for a catchment are given as$$\begin{array}{llllll} \text{Time (h)} & 0 & 1 & 2 & 3 & 4 \\ \text{Ordinate } (m^3/s) & 0 & 5 &...

Vehicles arriving at an intersection from one of the approach roads follow the Poisson distribution. The mean rate of arrival is $900$ vehicles per hour. If a gap is defi...

Consider the equation $\dfrac{du}{dt}=3t^2+1$ with $u=0$ at $t=0$. This is numerically solved by using the forward Euler method with a step size, $\Delta t=2$. The absolu...

A pre-tensioned rectangular concrete beam $150$ mm wide and $300$ mm depth is prestressed with three straight tendons, each having a cross-sectional are of $50 \: mm^2$, ...

Consider the stepped bar made with a linear elastic material and subjected to an axial load of $1$ kN, as shown in the figure.Segments $1$ and $2$ have cross-sectional ar...

The value of $M$ in the beam ABC shown in the figure is such that the joint B does not rotate.The value of support reaction (in kN) at B should be equal to _________.

Consider the beam ABCD shown in the figure.For a moving concentrated load of $50$ kN on the beam, the magnitude of the maximum bending moment (in kN-m) obtained at the su...

Consider two axially loaded columns, namely, $1$ and $2$, made of a linear elastic material with Young’s modulus $2 \times 10^5$ MPa, square cross-section with side $10$ ...

A column is subjected to a load through a bracket as shown in the figure.The resultant force (in kN, up to one decimal place) in the bolt $1$ is _______

A particle of mass $2$ kg is travelling at a velocity of $1.5$ m/s. A force $f(t) = 3t^2$ (in N) is applied to it in the direction of motion for a duration of $2$ seconds...

The activity details of a project are given below:$$\begin{array}{|c|c|c|} \hline \text{Activity} & \text{Depends on} & \text{Duration (in days)} \\ \hline P & \dots & 6 ...

It is proposed to drive H-piles up to a depth of $7$ m at a construction site. The average surface area of the H-pile is $3 \: m^2$ per meter length. The soil at the site...

The infinite sand slope shown in the figure is on the verge of sliding failure. The ground water table coincides with the ground surface. Unit weight of water $\gamma_w =...

A sluice gate used to control the flow in a horizontal channel of unit width is shown in the figure.It is observed that the depth of flow is $1.0$ m upstream of the gate,...

Water flows through a $90^{\circ}$ bend in a horizontal plane as depicted in the figure.A pressure of $140$ kPa is measured at Section $1-1$. The inlet diameter marked at...

A consolidated undrained $(\overline{CU})$ triaxial compression test is conducted on a normally consolidated clay at a confining pressure of $100$ kPa. The deviator stres...

An effective rainfall of $2$-hour duration produced of flood hydrograph peak of $200 \: m^3/s$. The flood hydrograph has a base flow of $20 \: m^3/s$. If the spatial aver...

The equivalent sound power level (in dB) of the four sources with the noise levels of $60$ dB, $69$ dB, $70$ dB and $79$ dB is ______

The spherical grit particles, having a radius of $0.01$ mm and specific gravity of $3.0$, need to be separated in a settling chamber. It is given that$g=9.81 \: m/s^2$the...

Two wastewater streams A and B, having an identical ultimate BOD are getting mixed to form the stream C. The temperature of the stream A is $20^{\circ}C$ and the temperat...

In newton-Raphson iterative method, the initial guess value $(x_{\text{ini}})$ is considered as zero while finding the roots of the equation: $f(x) = -2+6x-4x^2+0.5x^3$. ...

A horizontal beam $ABC$ is loaded as shown in the figure below. The distance of the point of contraflexure from end $A$ (in m) is _________

A nozzle is so shaped that the average flow velocity changes linearly from $1.5$ m/s at the beginning to $15$ m/s at its end in a distance of $0.375$m. The magnitude of t...

A groundwater sample was found to contain $500$ mg/L total dissolved solids (TDS). TDS (in $\%$) present in the sample is ________.

In a leveling work, sum of the Back Sight (B.S.) and Force Sight (F.S.) have been found to be $3.085$ m and $5.645$ m respectively. If the Reduced Level (R.L.) of the sta...

The probability density function of a random variable, $x$ is$f(x)= \begin{cases} \dfrac{x}{4} ( 4-x^2) & \text{ for } 0 \leq x \leq 2 \\ 0 & \text{ otherwise} \end{ca...

Consider the following second order linear differential equation$$\dfrac{d^2y}{dx^2} = -12x^2 +24 x – 20$$The boundary conditions are: at $x=0, \: y=5$ and at $x=2, \: y=...

For step-size, $\Delta x =0.4$, the value of following integral using Simpson’s $1/3$ rule is _______.$$\int_0^{0.8} (0.2 + 25 x – 200 x^2 + 675 x^3 – 900 x^4 +400 x^5) d...

A simply supported reinforced concrete beam of length $10$ m sags while undergoing shrinkage. Assuming a uniform curvature of $0.004 m^{-1}$ along the span, the maximum d...

A simply supported beam AB of span, $L=24$ m is subjected to two wheel loads acting at a distance, $d=5$ m apart as shown in the figure below. Each wheel transmits a load...