Recent questions tagged numerical-answers

A $16 \: mm$ thick gusset plate is connected to the $12 \: mm$ thick flange plate of an I-section using fillet welds on both sides as shown in the figure (not drawn to sc...

The network of a small construction project awarded to a contractor is shown in the following figure. The normal duration, crash duration, normal cost, and crash cost of ...

A box measuring $50 \: cm \times 50 \: cm \times 50 \: cm$ is filled to the top with dry coarse aggregate of mass $187.5 \: kg$. The water absorption and specific gravity...

A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a roller support at joint R. A point load of $50 \: kN$ is acting at joint in R in ...

A sample of air analysed at $0^{\circ} C$ and $1 \: atm$ pressure is reported to contain $0.02 \: ppm$ (parts per million) of $NO_2$. Assume the gram molecular mass of $N...

A $0.80 \: m$ deep bed of sand filter (length $4 \:m $ and width $3 \: m$) is made of uniform particles (diameter $=0.40 \: mm$, specific gravity $=2.65$, shape factor $=...

A wastewater is to be disinfected with $35 \: mg/L$ of chlorine to obtain $99 \%$ kill of micro-organisms. The number of micro-organisms remaining alive $(N_t)$ at time $...

A staff is placed on a benchmark (BM) of reduced level (RL) $100.000 \: m$ and a theodolite is placed at a horizontal distance of $50 \: m$ from the BM to measure the ver...

Consider the ordinary differential equation $x^2 \dfrac{d^2y}{dx^2} – 2x \dfrac{dy}{dx} +2y=0$. Given the values of $y(1)=0$ and $y(2)=2$, the value of $y(3)$ (round off ...

Average free flow speed and the jam density observed on a road stretch are $60 \: km/h$ and $120$ vehicles/km, respectively. For a linear speed-density relationship, the ...

Traffic on a highway is moving at a rate of $360$ vehicles per hour at a location. If the number of vehicles arriving on this highway follows Poisson distribution, the pr...

A parabolic vertical curve is being designed to join a road of grade $+5 \%$ with a road of grade $-3 \%$. The length of the vertical curve is $400 \: m$ measured along t...

Tie bars of $12 \: mm$ diameter are to be provided in a concrete pavement slab. The working tensile stress of the tie bars is $230 \: MPa$, the average bond strength betw...

The hyetograph of a storm event of duration $140$ minutes is shown in the figure:The infiltration capacity at the start of this event $(t=0)$ is $17 \: mm/hour$, which li...

Two water reservoirs are connected by a siphon (running full) of total length $5000$ m and diameter of $1.10$ m, as shown below (figure not drawn to scale).The inlet leg ...

Consider a laminar flow in the x-direction between two infinite parallel plates (Couette flow). The lower plate is stationary and the upper plate is moving with a velocit...

A reinforced concrete circular pile of $12 \: m$ length and $0.6 \: m$ diameter is embedded in stiff clay which has an undrained unit cohesion of $110 \: kN/m^2$. The adh...

A granular soil has a saturated unit weight of $20 \:kN/m^3$ and an effective angle of shearing resistance of $30^{\circ}$. The unit weight of water is $9.81 \: kN/m^3$. ...

A $3 \: m \times 3 \: m$ square precast reinforced concrete segments to be installed by pushing them through an existing railway embankment for making an underpass as sho...

The degree of static indeterminacy of the plane frame as shown in the figure is ________

The characteristic compressive strength of concrete required in a project is $25 \: MPa$ and the standard deviation in the observed compressive strength expected at site ...

The data from a closed traverse survey PQRS (run in the clockwise direction) are given in the table$$\begin{array}{|c|c|} \hline \text{Line} & \text{Included angle (in d...

A vehicle is moving on a road of grade $+4 \%$ at a speed of $20 \: m/s$. Consider the coefficient of rolling friction as $0.46$ and acceleration due to gravity as $10 \:...

The command area of a canal grows only one crop, i.e., wheat. The base period of wheat is $120$ days and its total water requirement, $\Delta$, is $40 \: cm$. If the cana...

Construction of a new building founded on a clayey soil was completed in January $2010$. In January $2014$, the average consolidation settlement of the foundation in clay...

A long uniformly distributed load of $10 \: kN/m$ and a concentrated load of $60 \: kN$ are moving together on the beam ABCD shown in the figure (not drawn to scale). The...

A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are $k_x = k_y = 5 \times 10^5 kN/m$ and $k_{\theta} =3 \times...

A rolled $I$-section beam is supported in a $75 \: mm$ wide bearing plate as shown in the figure. Thicknesses of flange and web of the $I$ section $20 \: mm$ and $8 \: mm...

When a specimen of $M25$ concrete is loaded to a stress level of $12.5 \: MPa$, a strain of $500 \times 10^{-6}$ is recorded. If this load is allowed to stand for a long ...

A water treatment plant treats $6000 \: m^3$ of water per day. As a part of the treatment process, discrete particles are required to be settled in a clarifier. A column ...

Raw municipal solid waste (MSW) collected from a city contains $70 \%$ decomposable material that can be converted to methane. The water content of the decomposable mater...

Consider the reactor shown in the figure. The flow rate through the reactor is $Q \: m^3/h$. The concentrations (in $mg/L$) of a compound in the influent and effluent are...

The uniform arrival and uniform service rates observed on an approach road to a signalized intersection are $20$ and $50$ vehicles/minute, respectively. For this signal, ...

A broad gauge railway line passes through a horizontal curved section (radius $=875 \:m$) of length $200 \: m$. The allowable speed on this portion is $100 \: km/h$. For ...

The speed-density relationship of a highway is given as $$u = 100 – 0.5 \: k$$ where, $u=$ speed in $km$ per hour, $k=$ density in vehicles per $km$. The maximum flow (in...

A confined aquifer of $15 \: m$ constant thickness is sandwiched between two aquicludes as shown in the figure (not drawn to scale).The heads indicated by two piezometers...

Two identical pipes (i.e., having the same length, same diameter, and same roughness) are used to withdraw water from a reservoir. In the first case, they are attached in...