Math & Nature   Suction feeding in the goliath grouper ◦ Given  Volume of the goliath grouper feeding mechanism at rest (t0) and at maximum expansion (t1)  Duration of the feeding event (t1 - t0)  Area of the mouth opening at maximum expansion (t1) 4) Find the velocity of water flow into the mouth of
View full slide show




Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e   Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a   N/A b   Cone B Length (mm) Area (mm2) a   Time 1 c     d   e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)   Volume (mm3)     Volume (mm3)   Volume (mm3)       0.132     
View full slide show




Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e  12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a   N/A b   Cone B Length (mm) Area (mm2) a   Time 1 c     d   e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)  195916.8 Volume (mm3)  84289.7  180206.5 Volume (mm3)   Volume (mm3)       0.132     
View full slide show




Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4   d  32.6 e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)   Volume (mm3)        0.132    
View full slide show




Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4   d  32.6 e  266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)  263547.1 Volume (mm3)  230974.7  494521.7  214315.3  0.132    
View full slide show




Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4  3338.8 d  32.6 e  266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)  263547.1 Volume (mm3)  230974.7  494521.7  214315.3  0.132 3338.8   
View full slide show




Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4  3338.8 d  32.6 e  266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)  263547.1 Volume (mm3)  230974.7  494521.7  214315.3  0.132 3338.8   486
View full slide show




Math & Nature  Fish feeding mechanisms ◦ Suction feeding  Goliath grouper Epinephelus itajara  Questions  What fluid velocity can the goliath grouper generate during suction feeding?  How does suction feeding by the goliath grouper compare to other fish?
View full slide show




Math & Nature  Goliath grouper model ◦ Objective  Determine the velocity of water flow into the mouth ◦ Procedure  Determine the volume of components A and B at rest (t0) and at maximum expansion (t1)  t0 = time at rest  t1 = time at maximum expansion A B  Determine the volume change during feeding A B
View full slide show




Snook Suction Feeding Cone A Length (mm) Area (mm2) a 2.1  N/A b  27.6 Cone B Length (mm) Area (mm2) a  2.1 Time 0 c  12.3 N/A d  1.8 e   Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  7.0 N/A b  28.9 Cone B Length (mm) Area (mm2) a  7.0 Time 1 c  12.3   d  5.9 e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)   Volume (mm3)     Volume (mm3)   Volume (mm3)        0.036    
View full slide show




Snook Suction Feeding Cone A Length (mm) Area (mm2) a 2.1  N/A b  27.6 Cone B Length (mm) Area (mm2) a  2.1 Time 0 c  12.3 N/A d  1.8 e 73.8  Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  7.0 N/A b  28.9 Cone B Length (mm) Area (mm2) a  7.0 Time 1 c  12.3  109.4 d  5.9 e  66.0 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 127.5  Volume (mm3)  147.2  274.7 Volume (mm3) 1482.9  Volume (mm3)  1611.5 3094.4   2819.7  0.036  109.4  716
View full slide show




Longjaw Butterfly Fish Suction Feeding Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 0 c 31.2 N/A d 1.1 e   Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 1 c 31.6   d 1.1 e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)   Volume (mm3)     Volume (mm3)   Volume (mm3)        0.022    
View full slide show




Longjaw Butterfly Fish Suction Feeding Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 0 c 31.2 N/A d 1.1 e  8.8 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 1 c 31.6  3.8 d 1.1 e  8.9 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 390.1  Volume (mm3)  1036.0  1426.1 Volume (mm3)  390.1 Volume (mm3)  1049.3  1439.4  13.3  0.022  3.8  159
View full slide show




Math & Nature  Suction feeding in the goliath grouper ◦ Given  Dimensions of cone B at maximum expansion (t1) 3) Find the area of the goliath grouper mouth at maximum expansion (t1).  A. Collins mouth
View full slide show




Math & Nature  Suction feeding in the goliath grouper ◦ Given  Dimensions of cones A and B at maximum expansion (t1) 2) Find the volume of the goliath grouper feeding mechanism at maximum expansion (t1).
View full slide show




Math & Nature  Suction feeding in the goliath grouper ◦ Given  Dimensions of cones A and B at rest (t0) 1) Find the volume of the goliath grouper feeding mechanism at rest (t0). b c a a e d
View full slide show




Math & Nature  Suction feeding in the goliath grouper ◦ Given  Dimensions of cones A and B at rest (t0) 1) Find the volume of the goliath grouper feeding mechanism at rest (t0). c b a a e d
View full slide show




Math & Nature  Goliath grouper model ◦ Objective  Determine the velocity of water flow into the mouth ◦ Procedure  Determine the area of the mouth at maximum expansion (t1)  t1 = time at maximum expansion A A B B
View full slide show