When it is threatened, a squid can escape by expelling a jet of water, sometimes

Question

When it is threatened, a squid can escape by expelling a jet of water,
sometimes colored with camou?aging ink. Consider a squid originally at rest in ocean water
of constant density ? = 1030 kg/m 3 . Its original mass is m 0 = 85.5 kg, of which a signi?cant
fraction is water inside its mantle. It expels this water through its siphon, a circular opening
of diameter d = 3.00 cm, at a speed of u = 15.0 m/s. (a) As the squid is just starting to
move, the surrounding water exerts no drag force on it. Find the squid’s initial acceleration.
(b) To estimate the maximum speed of the escaping squid, model the drag force of the
surrounding water as described by R = 1/2D?Av 2 . Assume that the squid has a drag
coe?cient of D = 0.300 and a cross-sectional area of A = 830 cm 2 . Find the speed at which
the drag force counterbalances the thrust of its jet.

Explanation / Answer

a)area of the circular opening A = d2/4 = (3x10-3)2/4= 7.07 x 10-4 m2

density = 1030 kg/m3

velocity u=15m/s

mass flow rate m' = Au = 10.923 kg/s

net force on the squid F= rate of change of momentum = m' u = 10.923 x 15 =163.85 N

acceleration = F/m =163.85/85.5 =1.92 m/s2

b) drag force R = 1/2 D A v2 = 1/2*0.3*830x10-4 V2 =124.5 x 10-4 V2

thrust =F =163.85 N

when F=R

=>   124.5 x 10-4 V2 = 163.85

=> V2 = 13160.6

=> V= 114.7 m/s

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