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. A simply supported beam of length 8 meters carries a uniformly distributed load of 1 0 kN / m and a point load of

. A simply supported beam of length 8 meters carries a uniformly distributed load of 10 kN/m and a point load of 20 kN at the center. Calculate the reactions at the supports and draw the shear force and bending moment diagrams.
Geotechnical Engineering:
A soil sample has a void ratio of 0.65 and a specific gravity of solids of 2.70. If the sample is fully saturated, calculate the moisture content and the bulk unit weight of the soil.
Hydraulics:
Water is flowing through a circular pipe of diameter 1 meter with a velocity of 3 m/s. Calculate the Reynolds number and determine whether the flow is laminar or turbulent if the kinematic viscosity of water is
1
1
0
6
2
/
110
6
m
2
/s.
Environmental Engineering:
A wastewater treatment plant treats 10,000 m^3/day of sewage. The influent has a BOD (Biochemical Oxygen Demand) of 300 mg/L. Calculate the amount of oxygen required per day to treat the sewage if the treatment efficiency is 90%.
Transportation Engineering:
A highway curve with a radius of 400 meters is designed for a speed of 100 km/h. Calculate the required super-elevation if the coefficient of lateral friction is 0.15.
Structural Dynamics:
A single-degree-of-freedom system has a mass of 500 kg and a stiffness of 2000 N/m. Calculate the natural frequency and the period of oscillation of the system.
Fluid Mechanics:
A rectangular channel of width 3 meters carries water with a depth of 2 meters and a velocity of 1.5 m/s. Calculate the flow rate and the Froude number. Determine whether the flow is subcritical or supercritical.
Concrete Technology:
A concrete mix design requires a water-cement ratio of 0.45. If 500 kg of cement is used, calculate the amount of water required. Also, if the mix design specifies a sand-to-aggregate ratio of 1:2.5, calculate the quantities of sand and aggregate needed.
Foundation Engineering:
A square footing of 2m x 2m is to be constructed on a sandy soil with an allowable bearing capacity of 200 kN/m^2. Calculate the maximum load the footing can support.
Water Resources Engineering:
A reservoir has an inflow rate of 10 m^3/s and a constant outflow rate of 7 m^3/s. Calculate the time required to fill the reservoir if its capacity is 2 million cubic meters..
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