Engineering Answers

Find by use of differentials the approximate total area of a right circular cone whose base radius and height are 5.03 inches and 11.89 inches, respectively.

A bridge 10-m wide is to be placed across a proposed underpass. This underpass is designed to have a grade of -4% and an ascending grade of +8%, where its vertex will be located at 4+420 with an elevation of 140m. It is required that the centerline of the bridge is exactly placed above the vertex of the curve, its bottom elevation is 148.10m and it should have a minimum vertical clearance of 6m under it.

a) Determine the length of the vertical parabolic curve.

b) Determine the location of the lowest point of the

curve.

c) Determine the elevation of the lowest point.

d) Determine the stationing and elevation of PC.

e) Determine the stationing and elevation of PT.

A natural gas-fired boiler operates with 20% excess air. Air is fed at 25 °C and contains 21% O2 and 79% N2 on a volume basis. Natural gas composition: 92.6% CH4, 3.6% C2H6, 0.8% C3H8, 0.3% C4H10, 2.6% N2, 0.1% CO2; GCV: 38.6 MJ/m3 . Molecular weights of C, H, O, N are 12 g, 1g, 16 g and 14 g respectively.

(i) During an energy audit, it was proposed to convert this boiler to a condensing boiler. Do you think it is a viable option? Why? In your discussion, consider the main aspects you should look at during the design and operating phases of a condensing boiler.

(ii) Calculate the amount of condensate formed if a condensing section is added to the boiler so that the flue gas exit temperature is 45 °C. Stack pressure is 1.013 bar.

(iv) Calculate the percentage total energy loss with the flue gas and condensate. The specific heat of the dry flue gas and condensate are 1.2 kJ/m3 K and 4.2 kJ/kg K respectively. Assume the molar volume of the gases as 22.4 m3 /kmol

Three rotating masses, A= 14 kg, B =11 kg and C =21 kg are attached to a shaft

with center of gravity 275 mm, 400 mm and 150 mm from the shaft axis. The

angular position of B and C are 60° and 135º measured in the same direction

from A. The distance between plane AB is 1.35 m, AC is 3.6 m and plane B is

between AC. Two balance masses are to be fitted between plane A B and BC

and the center of gravity of each mass is 225mm from the shaft axis.

calculate the magnitude of balance masses

.

Find the equation of straight line passing through the points (2, 3) and (3,



1).

Find the increment and differential of each of the following functions for the given values of the

variables and their increments.

𝑦 tan^-1 𝑥𝑦; 𝑥 = 2, 𝑦 = 0.5, ∆𝑥 = −0.05, ∆𝑦 = 0.01

Find the increment and differential of each of the following functions for the given values of the variables and their increments.

𝑥 ln 𝑦 + 𝑦 ln 𝑥; 𝑥 = 𝑦 = 1, ∆𝑥 = 0.01, ∆𝑦 = 0.02

Find by use of differentials the approximate total area of a right circular cone whose base radius

and height are 5.03 inches and 11.89 inches, respectively.

Find, approximately, the amount of metal in a closed tin can 3 inches in diameter and 5 inches

high, if the metal is 1/32 inches thick.

A volume of 0.36 m3 of air initially at a temperature of 20oC and a 03 pressure of 4bar is compressed reversibly and isothermally to a final

volume of 0.06m3. Calculate the mass, the final pressure, work done and

heat transfer. The specific heat and gas constant can be taken as 1kJ/kgK

and 287 J/kg