164 Ip(ay) o'2 KeIn IgfAy) Ke In Iptay) Igy) —vwn—— R1 =|) = Tgl)) Amp. ajo , IgQ2)e—Ww—> Igtho) Ke In Pa Biz? Ina o'1 Diff, Igihy) Tog) fain = Ipihy) € Ry Numerator Tythg}e- —wa— Ri © IofA,) i woe! we. Th) > Denominator Ir) Ke in Ipaq) € +! —| Diff. I] Ky In TpQy) +| Ty(A}) wt . Diff. Amp. Ry Xa Ke In ec) Bu2 Diff. Amp. +. a a Divider In yy) yoy) IpQ>) | ez, Tp (hy) Ke 9 A " Tp) Fig. 131,—-Cireuit diagram for providing a continuous reading of the mixing depth in the case of uniform mixing using twopairs of pyrheliometers, with one of the two pyrheliometers in each pair operating in one wave band and the other in a different wave band. “a = kz, where & is a constant and z is measured in the vertical direction with positive upward. The basic differential equation then becomes (see Figure 129) dl = —ywdb = —kzed L = —kz sec 6 dz. I Integrating between the limits of the top of the build- i i p 0 in ZZ Ip _ —k sec 02 Ty 2 or 2") = Iy exp (-a-5 — *(sec aep. 24 (24) Three Pyrheliometers at One Wave Band and One Zenith Distance If we use three pyrheliometers, each at a different level, it is possible to determine an effective height of We maythen write (23) I, = Ig exp {ne _f = @ \ where Zp = intensity of solar radiation at top of the mixing Jayer and z is measured from the top of the layer. If we express Ip = foe7* —(k/2) see @ z2 the mixing layer instantaneously and without filters under the assumption that the concentration decreases linearly with height. If we are dealing with a tall building, we may place one pyrheliometer at the ground denoted by subscript B; one at an intermediate level (JZ); and one at the top (T). (See Figure 132.) —k seco | zdz Ir = Ip exp {Eeeee a}, I> = Toe * (22) ing and the top of the mixing layer we have LF where 7, = the solar constant for all-band radiation, and @ is a constant, we have (25) ' or Ip = In exp( k o\ —a — 5 (cos aL (26)