An atrium has a cylindrical construction of diameter of 16 m and a height of 20 m. At the roof, the daylight can penetrate into the space through a ring (Area 2), as shown in Figure Q1. Area 1, with a diameter of 8 m, is an LED ceiling recessed luminaire. 3 4 2. Ring allowing daylight penetration Figure Q1 Illustration of the space dimension. (a) (i) If the roof ring is a diffuse panel with a transmittance of 0.6, calculate the direct illuminance at the center of the floor, given the illuminance on top of the roof is 20,000 lx. (6 marks) (ii) If the LED luminaire has a diffusing enclosure and produce a luminance of 2000 cd/m, calculate the direct illuminance at the center of the floor from the luminaire. (4 marks) (iii) What is the total luminous flux from the LED luminaire? If the luminaire is considered as a point source, calculate the direct illuminance at the center of the floor from the luminaire. (6 marks) (b) Write the flux balance equations, in terms of the exitance of the surfaces M, M2, M3, and M4, The reflectance p, P2, P3, P4 and the form factors form factors fi-j (i,j = 1 to 4). You do not need to give any numerical values. (4 marks) (c) Given f1-4 = 0.1339, f2-4 = 0.1194, p = 0.2, p2 = 0.5, p3= 0.5, P4 = 0.3, calculate the average illuminance at the floor surface. (5 marks)