4) (30 pts) Short Answers. a) Assume calcium ions need to diffuse from the outsi

Question

4) (30 pts) Short Answers. a) Assume calcium ions need to diffuse from the outside of a muscle cell to its center each time the muscle contracts. Given D 1 um'/ms and using a plausible distance of diffusion, estimate an animal's maximum heart rate (i.e., beats per minute). State assumptions. You may ignore unitless constants of order unity. b) At low Reynolds number, fluid flow is predominantly laminar. This means flow lines don't mix. Therefore a disturbance at one location travels quickly to another location. fish One problem with this is that as an organism lunges toward its prey, the prey senses the disturbance and is warned of the eminent attack. Certain fish have evolved a means of "attacking from a distance" by shooting a turbulent jet of water toward its prey. prey Assume the fish closes its mouth to a diameter of 1 mm while shooting the jet of water. Estimate the minimum velocity of the water iet.

Explanation / Answer

a) We know that elapsed time is given by t = x2/2D, where x is distance of diffusion, and D is difussion coefficient (which is given as 1micro.m/ms). Let assume distance x = 40 micro.m.

Then t = (40)2/(2*1) = 1600/2 = 800ms = 0.8s

Now, this t is the time for 1 beat. Therefore, for no. of bests per minute we will divide 60 by t.

So, the heart rate is 60/0.8 = 75 beats.min.

b) From Law of continuity that A*V = constant or A1V1 = A2V2 where A1 is the area of fish's mouth when it closes, A2 is the c-s area of fish's body (let's assume A2 is 8 time A1), and V1 is the velocity of water jet and V2 is the velocityspeed at which the fish is lunging towards prey.

Now V2 from above equation can be calculated as V1 = A2*V2/A1

By assumption A2/A1 = 8, therefore V1 = 8V2.

This means the minimum velocity of water jet should be 8 times the velocity at which the fish is chasing (or lunging towards) the prey.

Please note that your answer will be different if you assume different ratio of A2 and A1, however, the principle to calculate the water jet velocity will remain the same.

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