## FLv kv d

where d = pipe diameter (m). v = fluid velocity (m/s). L = length of pipe (m). k = friction head (m). f = friction factor.

The friction factor, f, is equal to f = 64/Re for Re < 2000 f = 0.032 for Re > 2000

The friction head of various parts of the circuit can be estimated by using the data given in Table 5.2.

The friction factor for the developing flow in the connecting pipes and collector risers is given by f = 1 +

0.038

0.964

 Parameter k Value Entry from tank to connecting pipe to collector 0.5 Losses due to bends in connecting pipes Right-angle bend Equivalent length of pipe increased by 30d for Re < 2000 or k = 1.0 for Re > 2000 45° bend Equivalent length of pipe increased by 20d for Re < 2000 or k = 0.6 for Re > 2000 Cross-section change at junction of connecting pipes and header Sudden expansion k = 0.667(dj/d2)4 - 2.667 (dj/d2)2 + 2.0 Sudden contraction k = —0.3259(d2/dj)4 - 0.1784 (d2/dj)2 + 0.5 Entry of flow into tank 1.0 Note: For pipe diameters, dj = inlet diameter and d2 = outlet diameter.

The collector header pressure drop, Ph, is equal to the average of pressure change along inlet and outlet headers for equal mass flow in each riser, given by

1 2dh where, from Eq. (5.8a), f = 64/Re (Re based on inlet header velocity and temperature) and

Based on the outlet header velocity and temperature,

Finally,

To model the complete system, the interaction of the storage tank is required. This is modeled with the fully stratified storage tank model, which is presented in Section 5.3.3.

The procedure to model the complete system is as follows. Initially, the temperature distribution around the thermosiphon loop for the flow rate of the previous time step is evaluated. The inlet temperature to the collector is computed from the bulk mean temperature of the segments in the bottom of the tank with a volume equal to the collector volume flow (see Section 5.3.3). After allowance for heat loss from the inlet pipe, with Eq. (5.7), is made, the temperature of each of the Nc fixed nodes used to represent the collector temperature profile is evaluated from Eq. (5.2). Finally, the temperature of the new fluid segment returned to the tank is computed from the collector outlet temperature and the temperature drop across the return pipe to the tank. A new tank temperature profile is then evaluated (see Section 5.3.3).

The thermosiphon pressure head due to density differences around the loop is determined from the system temperature profile. The difference between the friction pressure drop around the circuit and the net thermosiphon pressure is evaluated for this flow rate. These values and those from the previous calculation, for the flow rate and net difference between the friction and static pressures, are then used to estimate the new flow; this process is repeated until Eq. (5.1) is satisfied. This procedure is not suitable for hand calculations, but it is relatively easy to do with a computer.