L1. Pressure driven flow in a cylindrical tube. You would like to understand how much blood is able to pass through a typical artery in your brain and quantify how plaque build up in these arteries is decreasing the blood flow. Assume these arteries are cylindrical and the blood can be called a Newtonian fluid. a) Draw a diagram of your system, mark all boundaries, and choose a coordinate system. b) Convert the following momentum balance to the mathematical equation that governs 1dimensional pressure-driven flow in a cylindrical tube. [Rateofmomentumaccumulation]=[Rateofmomentumflowin][Rateofmomentumflowout]+[Sumofallforces] c) Integrate the equation and solve for the velocity profile. You will need to use the constitutive relationship for a Newtonian fluid in cylindrical coordinates =drdv2. d) State your boundary conditions and then obtain an expression for velocity. e) Using your expression for velocity and the equation for volumetric flow rate Q=vndA, solve for Q to obtain the volumetric flow rate for pressure driven flow in a cylindrical tube (a.k.a. Hagen-Poiscuille's Law). f) If the plaque build-up decreases the radius of the brain arteries by 5% how mueh in the drop in the blood flow rate