Scenario

The design and development department associated with a power generation plant has various issues which require resolving, you are now asked to provide an analysis of these issues with respect to the questions detailed below:

Task 1:

The electric current I drawn from a motor comes from two sources I₁ and I₂ and are given by

I₁ = 2 sin (t - Π/3) and I₂ = cos (t - Π/3). Find analytically, the resultant current I in the form Rsin( θ + α) given that I = I₁ + I₂.

Task 2:

Discharged cooling water from a condenser flows in a 450mm diameter drain to a height of 175mm. Calculate the wetted perimeter of the drain and the cross sectional area of water.

Task 3:

During a heat transfer analysis the use of several trigonometric and hyperbolic functions is required.

(a) Find the value of sinh 4.45 to four decimal places using the exponential form. Check your result using the series for sinhx x to the sixth term.

(b) Show that sin(x + Π/3) + sin(x + 2Π/3) = √3 cosx

(c) Using the formula tanhx = (e^x -e^-x)/(e^x +e^-x) find the values of x that satisfy the equation x = tanh^-1(-0.5)

(d) At various operating timess the sinusiodal voltage from two transformation V₁ & V₂ are required to be combined. Use graphical addition to find the resulant voltage V_R. Check the validity of your result using an analytical method given that V₁ = 3sinθ and V₂ = 5sin(θ - 30^o)