Recent questions tagged numerical-answers

The specific gravity of a soil is $2.60$. The soil is at $50 \%$ degree of saturation with water content of $15 \%$. The void ratio of the soil is _______.0.350.780.871.2...

A group of $9$ friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter $300 \mathrm{~mm}$ and length $7 \mathrm...

A student is scanning his $10 \text { inch } \times 10 \text { inch}$ certificate at $ 600 \text { dots per inch (dpi)}$ to convert it to raster. What is the percentage r...

The probabilities of occurrences of two independent events $\text {A}$ and $\text {B}$ are $0.5$ and $0.8,$ respectively. What is the probability of occurrence of at leas...

Consider the fillet-welded lap joint shown in the figure (not to scale). The length of the weld shown is the effective length. The welded surfaces meet at right angle. Th...

A canal supplies water to an area growing wheat over $100$ hectares. The duration between the first and last watering is $120$ days, and the total depth of water required...

Consider the horizontal axis passing through the centroid of the steel beam cross-section shown in the figure. What is the shape factor (rounded off to one decimal place)...

Consider the pin-jointed truss shown in the figure (not to scale). All members have the same axial rigidity, $A E$. Members $\mathrm{QR}, \mathrm{RS}$, and $\mathrm{ST}$ ...

Consider that a force $\text{P}$ is acting on the surface of a half-space (Boussinesq's problem). The expression for the vertical stress $\left(\sigma_{z}\right)$ at any ...

A jet of water having a velocity of $20 \mathrm{~m} / \mathrm{s}$ strikes a series of plates fixed radially on a wheel revolving in the same direction as the jet at $15 \...

The differential equation,$$\frac{\mathrm{d} u}{\mathrm{~d} t}+2 t u^2=1,$$is solved by employing a backward difference scheme within the finite difference framework. The...

The infinitesimal element shown in the figure (not to scale) represents the state of stress at a point in a body. What is the magnitude of the maximum principal stress (i...

An idealised bridge truss is shown in the figure. The force in Member $U_2 L_3$ is $\mathrm{kN}$__________ (round off to one decimal place).

The cross-section of a girder is shown in the figure (not to scale). The section is symmetric about a vertical axis $(Y-Y).$ The moment of inertia of the section about th...

A soil having the average properties, bulk unit weight $=19 \mathrm{~kN} / \mathrm{m}^3$; angle of internal friction $=25^{\circ}$ and cohesion $=15 \mathrm{~kPa}$, is be...

A smooth vertical retaining wall supporting layered soils is shown in figure. According to Rankine's earth pressure theory, the lateral active earth pressure acting at th...

A vertical trench is excavated in a clayey soil deposit having a surcharge load of $30 \mathrm{~kPa}$. A fluid of unit weight $12 \mathrm{~kN} / \mathrm{m}^3$ is poured i...

A $12$-hour storm occurs over a catchment and results in a direct runoff depth of $100 \mathrm{~mm}.$ The time-distribution of the rainfall intensity is shown in the figu...

A hydraulic jump occurs in a $1.0 \mathrm{~m}$ wide horizontal, frictionless, rectangular channel, with a pre-jump depth of $0.2 \mathrm{~m}$ and a post-jump depth of $1....

In Horton's equation fitted to the infiltration data for a soil, the initial infiltration capacity is $10 \mathrm{~mm} / \mathrm{h}$; final infiltration capacity is $5 \m...

The composition and energy content of a representative solid waste sample are given in the table. If the moisture content of the waste is $26 \%$, the energy content of t...

A flocculator tank has a volume of $2800 \mathrm{~m}^{3 .}$ The temperature of water in the tank is $15^{\circ} \mathrm{C}$, and the average velocity gradient maintained ...

The wastewater inflow to an activated sludge plant is $0.5 \mathrm{~m}^3 / \mathrm{s}$, and the plant is to be operated with a food to microorganism ratio of $0.2 \mathrm...

Trigonometric levelling was carried out from two stations $\mathrm{P}$ and $\mathrm{Q}$ to find the reduced level ($\text{R. L.}$) of the top of hillock, as shown in the ...

The function $f(x,y)$ satisfies the Laplace equation $$\bigtriangledown^{2}f(x,y) = 0$$on a circular domain of radius $r=1$ with its center at point $P$ with coordinates$...

$\displaystyle{}\int \left( x-\frac{x^{2}}{2} + \frac{x^{3}}{3} – \frac{x^{4}}{4} + \dots \right) dx$ is equal to$\frac{1}{1+x} + $ Constant$\frac{1}{1+x^{2}} + $ Consta...

Read the following statements relating to flexure of reinforced concrete beams:In over-reinforced sections, the failure strain in concrete reaches earlier than the yield ...

Stresses acting on an infinitesimal soil element are shown in the figure (with $\sigma_{z} \sigma_{x}$). The major and minor principal stresses are $\sigma_{1}$ and $\si...

In a certain month, the reference crop evapotranspiration at a location is $6 \; \text{mm/day.}$ If the crop coefficient and soil coefficient are $1.2$ and $0.8,$ respect...

The dimension of dynamic viscosity is:$\text{ML}^{-1} \text{T}^{-1}$$\text{ML}^{-1} \text{T}^{-2}$$\text{ML}^{-2} \text{T}^{-2}$$\text{ML}^{0} \text{T}^{-1}$

A process equipment emits $5 \; \text{kg/h}$ of volatile organic compounds $\text{(VOCs)}$. If a hood placed over the process equipment captures $95\%$ of the $\text{VOCs...

If the magnetic bearing of the Sun at a place at noon is $\text{S} \; 2^{\circ} \; \text{E},$ the magnetic declination (in $\textbf{degrees}$) at that place is$2^{\circ} ...

The error in measuring the radius of a $5 \; \text{cm}$ circular rod was $0.2 \%.$ If the cross-sectional area of the rod was calculated using this measurement, then the ...

The components of pure shear strain in a sheared material are given in the matrix form:$$ \varepsilon = \begin{bmatrix} 1 & 1 \\ 1 & – 1 \end{bmatrix}$$Here, $\text{Trace...

The inside diameter of a sample tube is $50 \; \text{mm}.$ The inside diameter of the cutting edge is kept such that the Inside Clearance Ratio $\text{(ICR)}$ is $1.0 \%$...

A concentrically loaded isolated square footing of size $2 \; \text{m} \times 2 \; \text{m}$ carries a concentrated vertical load of $1000 \; \text{kN}.$ Considering Bous...