Volume of Fish Swim Bladder to Achieve Neutral Buoyancy
Df = Mf / Vt where: Df is the density of the fish Mf is the mass of the fish Vt is the total volume of the fish. but, Vt = Vf(wosb) + Vsb where: Vf(wosb) is the volume of the fish without the volume of swim bladder gas Vsb is the volume of swim bladder gas. and, Mf = Dft _ Vf(wosb) + Dair _ Vsb where: Dft is the density of fish tissue Dair is the density of air. Since the density of air is 3 orders of magnitude less than the density of fish and Vsb is an order of magnitude less than Vf(wosb), Mf = Dft _ Vf(wosb) For neutral buoyancy, Df = 1.0, independent of depth. Thus, Df = 1.0 = Dft _ Vf(wosb) / (Vf(wosb) + Vsb) Dft _ Vf(wosb) = Vf(wosb) + Vsb or Vsb = (Dft - 1) _ Vf(wosb) = (Dft - 1) _ (Vt - Vsb) Dividing both sides by Vt yields: Vsb / Vt = (Dft - 1) _ [1 - (Vsb / Vt)] or Vsb / Vt = (Dft - 1) / [1 + (Dft - 1)] According to Harvey (1963), the density of sockeye fish tissue is 1.0634 g/ml. Therefore, for neutral buoyancy at any depth, Vsb / Vt = 0.596 or 5.96%.
