FISHERY BULLETIN: VOL. 72, NO. 4 



0.0 02 0.4 0.6 



0.8 1.0 1.2 



L{cm) 



1.4 



1.6 



Figure 5. — Cross sectional area of larval anchovy head, A^ , as a 

 function of length L. 



roughly ellipsoidal or a bluff body, I decided to 

 modify, with due consideration for the geomet- 

 ric differences, the drag relationship observed 

 for a copepod (Lahidocera trispinosa), w^hich is a 

 naturally occurring bluff body of similar shape, 

 to represent the relevant characteristics of the 

 anchovy larvae head. 



If the copepod is taken as an equivalent ellip- 

 soid, we get, from data in Vlymen (1970), 



(e) - '■'■ 



where a,, is the major axis length and b^ is the 

 semimajor axis length of the copepod L. tri- 

 spinosa and is given respectively by a^ = -^^ 



m 



(one-half the metasome length) and b, 



For the anchovies studied -j- = 0.155 (Figure 4) 

 and fori = 1^4cmandA;/ = 0.007 cm^,/;/ = 0.217 

 cm yielding /^\ = 2.3. 



For high Reynolds numbers (~10 -10 ) and 

 rotationally symmetrical bluff bodies of various 

 l/d ratios, where I is the bluff body length and d is 

 diameter, we have 



(Hoerner, 1965) 



where Cf is the frictional drag coefficient based 

 on wetted surface area and Cp. is the drag 

 coefficient based on frontal area. We can use 

 this relation to approximate C^. (lid =2.9) as- 



Co- Wd =2.3) 

 suming Cfdid = 2.9) = Cfilld = 2.3), and use 

 the above ratio to modify the measured drag re- 

 lation already obtained for the copepod. Sub- 

 stituting lid = 2.9 and lid = 2.3 into the rela- 

 tion for CoJCf we get on dividing 



Cp . (lid = 2.9) ^ ^^ 



Cd  (lid = 2.3) 

 At lower Reynolds numbers we expect the 

 geometric differences to cause a greater 

 discrepancy between Cp (lid = 2.9) and Cp (lid 

 = 2.3). In particular Cp (lid = 2.9)> Cp(lld = 

 2.3). However, since in my experiments Re was 

 from 0- to 100, the region where we expect the 

 Cp (Re) curve to flatten out to a fairly constant 

 value we take Cp (Re) for the copepod as a first 

 approximation to the Cp (Re) for the anchovy 

 head. That function is Cp (Re) = 85.2/Re-8o, 

 Vlymen (1970). The virtual mass,- m, occurring 

 in the integrals for W^ is then calculated by 

 considering the head as if it were an equivalent 

 ellipsoid. Using (ajba) = 2.3 we can calculate 



m as m = kj p Vp where k^ 



J 



(2 -7) 



7 = 2 



(i#) •" "• m) 



i - S)" 



V^ = 4/37ra„6„2 Vlymen (1970). 



For a 1.4-cm larva m has a value of 1.80 x 10^^ g 

 and assuming the head density is the same as 

 seawater we get M = 7.9 x lO"'* g. Thus Wf^ 

 may be rewritten as 



W„ = 1/2 



•^ 



80 



vrA,,dt 



■I 



4dV, 

 (9.7 xlO -^V,dt 



892 



