Determine the angle a for cosa = sina . Solution If sin a = cos a means that the angles of the triangle are equal, too, so, in a right angle triangle, the angles could only be of 45 degrees. This conclusion is based on fact that in a triangle, the sum of angles is 180 degrees, so, if one of them is 90 degrees and the other 2 are equals, their measure could only be of 45 degrees. We\'ll prove this solving the equation: sin a - cos a=0 We could divide the equation by (cos a) and the result will be: sin a /cos a - 1 =0 But we know that the ratio between sina and cos a determine the tangent function. tg a -1 =0 We\'ll add 1 both sides: tg a = 1 a= arctg 1 + k*pi a = pi/4 + k*pi a = pi/4=45 degrees. a = 45 degrees.

1. determine the equivalent diameter and preasure drop for 5000 CFM of air flowing through a
rectangular duct of dimensions 18 in*24 in that is 30 ft long.
Solution
We know that the equivalent diameter (D)= 4*Area/ Perimeter
D = 4ab/ 2(a+b) where a and b are the dimensions of the rectangular duct
D = 4*18*24 /2(18+24) = 20.57 ft
Now we have to calculate the pressure drop through the pipe
Q = AV where Q is discharge , A is area of the duct , V is the velocity of the fluid thorugh the
pipe
V= Q/A = 5000/(18*24 ) = 11.57 ft/min
We know that pressure drop (dP ) = 32uVL / D2 where u is viscosity of air.
Hence on putting the value we can calculate the value of pressure drop
Since the value of viscosity of air therefore we will use the standard value of it.
And on putting the value we can calcualte it.