Multiply the equivalent length of a gate valve by K(ball valve)/K(gate valve).
References to 17th edition, 1st printing
L=KD/f (pg 3-110)
D and f would be constants for both conditions, gate valve and Ball valve. Only variable is K.
Use "Friction loss of water in pipe fittings in terms of equivalent length (L) feet of pipe" (pg 3-120) for eq len of gate valve.
Use "Friction Loss in Pipe fittings" on pg 3-111 (chart of K values) for the K values for gate valve and ball valve.
Example: Determine eq length of gate valve based on 90-deg bend, 6" diamter pipe (these fittings are in both tables)
K(gate valve)/K(bend) = 0.12/0.45 = 0.267
Eq Len(90 bend) = 15.2 ft; Calc'd Eq Len (gate valve) = 15.2*0.267 = 4.06 ft
From pg 3-120:
Eq Len (gate valve) = 4.04 ft