Question

why bio medical engineers study fluid mechanics...

Answer 1

Not an expert on the topic but I do have a little knowledge.

Fluid Mechanics is one of the most exciting areas of biomedical research and medical diagnostics today. Microfluidics and Nanofluidics are being studied heavily, to understand how fluids behave and flow at small scales. Many research labs in universities, and companies involved in biomedical devices/medical diagnostics will have people working on the above areas without a doubt. 

There's tons of fluid dynamics related stuff happening in your body right now. Viscous flow, flow through small capillaries, osmosis, flow through membranes and filters, pumping action and lots of other stuff! 

Studying the properties of fluids at such small scales helps us design better medical instruments, such as syringe needles (in fact I think there's a whole class of microfluidic syringes), pumps for various applications, and LoC (Lab on Chip) devices {which are gaining popularity now}. Ongoing research is also aimed at creating highly precise dosage systems, other methods of drug delivery, and in achieving low cost diagnostic procedures/instruments. 

Besides this you also have current medical equipment using principles of fluid dynamics - respirators, pumps, ventilators, dialysis equipment (etc)