Recent questions tagged numerical-answers

A $5\: m$ high vertical wall has a saturated clay backfill. The saturated unit weight and cohesion of clay are $18\: kN/m^3$ and $20\: kPa$, respectively. The angle of in...

A cast iron pipe of diameter $600\: mm$ and length $400\: m$ carries water from a tank and discharges freely into air at a point $4.5\: m$ below the water surface in the ...

A hydraulic jump occurs in a triangular $\text{(V-shaped)}$ channel with side slopes $1:1$ (vertical to horizontal). The sequent depths are $0.5\: m$ and $1.5\: m$. The f...

A concrete dam holds $10\: m$ of static water as shown in the figure (not drawn to the scale). The uplift is assumed to vary linearly from full hydrostatic head at the he...

A waste to energy plant burns dry solid waste of composition: Carbon $= 35\%$, Oxygen $= 26\%$ , Hydrogen $= 10\%$, Sulphur $= 6\%$, Nitrogen $= 3\%$ and Inerts $= 20\%.$...

A sample of water contains an organic compound $C_8H_{16}O_8$ at a concentration of $10^{-3}\: \text{mol/litre}$. Given that the atomic weight of $C = 12\: \text{g/mol}, ...

A theodolite is set up at station $A$. The $RL$ of instrument axis is $212.250\: m$. The angle of elevation to the top of a $4\: m$ long staff, held vertical at station $...

For a construction project, the mean and standard deviation of the completion time are $200$ days and $6.1$ days, respectively. Assume normal distribution and use the val...

The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________

A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the c...

A sheet pile has an embedment depth of $12$ m in a homogeneous soil stratum. The coefficient of permeability of soil is $10^{-6} m/s$. Difference in the water levels betw...

The VPI (vertical point of section) is $100$ m away (when measured along the horizontal) from the VPC (vertical point of curvature). If the vertical is parabolic, the len...

During a storm event in a certain period, the rainfall intensity is $3.5$ cm/hour and the $\Phi$-index is $1.5$ cm/hour. The intensity of effective rainfall (in cm/hour, ...

The infiltration capacity of a soil follows the Horton’s exponential model, $f=c_1+c_2e^{-kt}$. During an experiment, the initial infiltration capacity was observed to be...

While aligning a hill road with a ruling gradient $6\%$, a horizontal curve of radius $50 \: m$ is encountered. The grade compensation (in percentage, up to two decimal p...

Two towers, A and B, standing vertically on a horizontal ground, appear in a vertical aerial photograph as shown in the figure.The length of the image of the tower A on t...

A hallow circular shaft has an outer diameter of $100 $ mm and inner diameter of $50 $ mm. If the allowable shear stress is $125$ MPa, the maximum torque (in kN-m) that t...

A simply supprted rectangular concrete beam of span $8$ m has to be prestressed with a force of $1600$ kN. The tendon is of parabolic profile having zero eccentricity at ...

Two plates od $8$ mm thickness each are connected by a fillet weld of $6$ mm thickness as shown in the figure. The permissible stresses in the plate and the weld are $150...

Consider the portal frame shown in the figure and assume the modulus of elasticity, $E=2.5 \times 10^4$ MPa and the moment of inertia, $I= 8 \times 10^8 \: mm^4$ for all ...

A $2$ m long, axially loaded mild steel rod of $8$ mm diameter exhibits the load-displacement $(P-\delta)$ behavior as shown in the figure.Assume the yield stress of stee...

Consider a square shaped area ABCD on the ground with its centre at M as shown in the figure. Four concentrated vertical loads of $P=5000$ kN are applied on this area, on...

The figure shows a U-tube having a $5 \: mm \times 5 mm$ square cross-section filled with mercury (specific gravity $13.6$) up to a height of $20 $ cm in each limb (open...

A $1$ m wide rectangular channel carries a discharge of $2 \: m^3 /s$. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that ...

A catchment is idealized as a $25 \: km \times 25 \: km$ square. It has five rain gauges, one at each corner and one at the corner, as shown in the figure.During a month,...

The culturable command area of a canal is $10.000$ ha. The area grows only two crops – rice in the Kharif season and wheat in the Rabi season. The design discharge of the...

Water is pumped at a steady uniform flow rate of $0.01 \: m^3/s$ through a horizontal smooth circular pipe of $100$ mm diameter. Given that the Reynolds number is $800$ a...

The composition of a municipal solid waste sample is given below:$\begin{array}{|l|c|c|c|} \hline \text{Component} & \text{Percent by} & \text{Moisture Content} & \text{E...

For a given water sample, the ratio between BOD$_{\text{5-day, 20}^{\circ} C}$ and the ultimate BOD is $0.68$. The value of the reaction rate constant $k$ (on base $e$) (...

A municipal corporation is required to treat $1000 \: m^3/day$ of water. It is found that an overflow rate of $20 m/day$ will produce a satisfactory removal of the discre...

The analysis of a water sample produces the following results:$\begin{array}{|c|c|c|} \hline \text{Ion} & \text{milligram per milli-equivalent} & \text{Concentration} \\ ...

The radii of relative stiffness of the rigid pavements P and Q are denoted by $l_P$ and $l_Q$, respectively. The geometric and material properties of the concrete slab an...

An observer standing on the deck of a ship just sees the top of a lighthouse. The top of the lighthouse is $40$ m above the sea level and the height of the observer’s eye...

For a given loading on a rectangular plain concrete beam with an overall depth of $500 \: mm$, the compressive strain and tensile strain developed at the extreme fibers a...

A completely mixed dilute suspension of sand particles having diameters $0.25, \: 0.35, \: 0.40, \: 0.45$ and $0.50 \: mm$ are filled in a transparent glass column of dia...

The maximum number of vehicles observed in any five minute period during the peak hour is $160$. If the total flow in the peak hour is $1000$ vehicles, the five minute pe...

A circular duct carrying water gradually contracts from a diameter of $30 \: cm$ to $15 \: cm$. The figure (not drawn to scale) shows the arrangement to differential man...

The probability that the annual maximum flood discharge will exceed $25000 \: m^3/s$, at least once in next $5$ years is found to be $0.25$. The return period of this flo...

A soil has specific gravity of its solids equal to $2.65$. The mass density of water is $1000 \: kg/m^3$. Considering zero air voids and $10 \%$ moisture content of the s...

A concentrated load of $500 \: kN$ is applied on an elastic half space. The ratio of the increase in vertical normal stress at depths of $2 \: m$ and $4 \: m$ along the p...