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Solve d^{2}y/dx^{2}-6dy/dx+13y=20e^{3x}cos(2x+5)


Solve the initial value problem y^{2}y -y^{3}tanx=sinxcos^{2}x,y(0)=1


the tunction f(z)= (z)^{2}/z,z≠0 0,z=0 suntistes -Rieman equations at z=0 Does f (0) exist?`


Evaluate ∫0^{π/2α}αsinαxdx,α>0 by using Leibniz formula.`


find the length of the curve y=ln(e^{x}+1/e^{x}-1) from x=1 to x=2 `


a short reinforced concrete column of section 200mm ×220mm is to be reinforce with 4 number steel bars and is required to carry n axial load of 850kn. the stress in the concrete must not exceed 7n/mm^2 and the stress in the steel must not exceed 150n/mm^2. determine the diameter required for the bars and the subsequent stresses occuring in the concrete and the steel under the specified load.[ young's modulus; concrete =14kn/mm^2, steel =210kn/mm^2]

A 3 cm diameter tube is used to measure the binary diffusion coefficient of water vapor in air at

20°C at an elevation of 1600 m where the atmospheric pressure is 83.5 kPa. The tube is partially

filled with water, and the distance from the water surface to the open end of the tube is 40 cm.

Dry air is blown over the open end of the tube so that water vapor rising to the top is removed

immediately and the concentration of vapor at the top of the tube is zero. In 15 days of

continuous operation at constant pressure and temperature, the amount of water that has

evaporated is measured to be 1.23 g. Determine the diffusion coefficient of water vapor in air at

20°C and 83.5 kPa. Given, the pressure of water at 20°C is 2.34 kPa.


A lab technician, working in a lab has poured liquid chloroform into a test tubes with inner 

diameter of 25 mm. The test tube holds an amount of 29.46 cm3

liquid chloroform at a level of

1 cm from the top (Figure 2). The chloroform molecular weight and vapor pressure is 119.38 

kg/kmol and 21 kPa respectively. The evaporation of chloroform to the surrounding air is 

occurring at 25 C and 1 atm. If the diffusion coefficient of chloroform in air is DAB is 0.104 cm2

/s, 

determine the rate of evaporation and the time taken for half of the chloroform to be evaporated

at the stated condition. Given the density of the chloroform is 1.49 g/cm³.


An 8 cm internal diameter with 30 cm high pitcher half filled with water is left in a dry room at 

15°C and 87 kPa with its top open. If the water is maintained at 15°C at all times, determine how 

long it will take for the water to evaporate completely. Given, the saturation pressure of water 

at 15°C is 1.705 kPa


a horizontal tube carrying hot water has a surface temperature of 355.4 K and the outside diameter of 25.4 mm. The tube is exposed to room air at 294.3 K. Calculate the nature convection heat loss for a 1 m length of pipe. if the tube is replaced with two horizontal plate and the bottom plate is hotter than the upper plate. compared the resulted value of natural convection heat loss using tube and plate


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