Structural Design:

A reinforced concrete beam with a rectangular cross$-$section of width $300$ mm and depth $500$ mm is reinforced with $4$ steel bars of diameter $20$ mm$.$ The grade of concrete is M$25,$ and the steel is Fe$500.$ Calculate the ultimate moment capacity of the beam.

Geotechnical Engineering:

A retaining wall is $5$ meters high and retains a granular backfill with a unit weight of $18$ kN$/$m$^3$ and an internal friction angle of $30.$ Calculate the lateral earth pressure at the base of the wall using Rankine$$s theory.

Hydrology:

A catchment area of $50$ km$^2$ receives a uniform rainfall of $20$ mm$/$hr for $5$ hours. Calculate the total runoff volume if the runoff coefficient is $0\mathrm{.}6.$

Structural Analysis:

A propped cantilever beam of length $6$ meters is subjected to a uniformly distributed load of $15$ kN$/$m$.$ Calculate the reactions at the supports and the bending moment at the fixed end.

Environmental Engineering:

A trickling filter in a wastewater treatment plant treats an influent with a BOD of $200$ mg$/$L$.$ The filter has a volume of $1000$ m$^3$ and the hydraulic loading rate is $10$ m$^3/$m$^2.$day. Calculate the BOD removal efficiency if the filter media has a specific surface area of $120$ m$^2/$m$^3.$

Transportation Engineering:

Design a vertical curve connecting two road gradients of $+3\%$ and $-2\%.$ The design speed is $80$ km$/$h$,$ and the minimum sight distance required is $160$ meters. Calculate the length of the vertical curve.

Water Supply Engineering:

A water distribution system has a pipeline of diameter $300$ mm and length $2$ km$.$ The head loss due to friction is $15$ meters. Calculate the flow rate using the Darcy$-$Weisbach equation. Assume the friction factor

$$

f is $0\mathrm{.}02.$

Concrete Technology:

A concrete mix requires a compressive strength of $40$ MPa at $28$ days. If the standard deviation of the mix is $5$ MPa, calculate the required mean strength of the concrete using a factor of safety of $1\mathrm{.}65.$

Foundation Engineering:

A circular footing with a diameter of $1\mathrm{.}5$ meters is to be constructed on a clayey soil with an undrained shear strength of $100$ kN$/$m$^2.$ Calculate the bearing capacity of the footing using Terzaghi$$s bearing capacity equation.

Fluid Mechanics:

A venturi meter with a throat diameter of $100$ mm is installed in a pipeline of diameter $200$ mm carrying water. The differential pressure head is $0\mathrm{.}5$ meters. Calculate the flow rate through the pipeline. Assume the coefficient of discharge is $0\mathrm{.}98.$

Why we need to understand the operating system