physics about fluids

1. Equating pressure at level marked ab in the diagram,
(27.2/100).d.g = [(27.2-9.41)/1000].(1000).g
where d is the density of oil and g is the acceleration due to gravity
hence, d = (17.79/27.2).(1000) kg/m3 = 654 kg/m3

2. Using Poiseuille's Equation,
V/t = pi.(0.71x10^-3x10^5).(a)^4/(8 x 0.018x10^-3 x 21) m^3/s
where pi = 3.14159....
a is the radius of the duct
V is the volume of air passing through the duct within time interval t

Since volume of room = 9 x 14 x 4 m^3 = 504 m^3
Rate of air flow V/t = 504/(10x60) m^3/s = 0.84 m^3/s

Hence, 0.84 = pi.(0.71x10^-3x10^5).(a)^4/(8 x 0.018x10^-3 x 21)
solve for a. The diameter of the duct = 2a.