Question 2 An artery has a length L and an internal diameter Dr. A build-up of plaque causes a narrowing halfway along the artery (as shown in Figure QB), which can be modelled as an obstruction with a viscous loss coefficient K₁₁. La Da Figure Q2: Flow along an artery with a obstruction (top), and flow along the same artery after a stent has been implanted (bottom). Clinicians consider performing surgery to insert a stent, which would go inside the artery and hold it open and removing the effect of the blockage, as shown in Figure Q2. The stent would have a length L, and the entry and exit to the stent would have both have a loss coefficient of K₁₂. You may assume that the flow is laminar. a) Find an expression for the pressure drop in the artery if no blockage or stent were present? [4 marks] b) Find an expression for the pressure drop after the blockage has developed? [4 marks] c) Find an expression for the pressure drop after the stent has been inserted? [7 marks] d) Clinicians will not insert stents unless they reduce the pressure drop along the artery. Find an expression for the minimum loss coefficient for the blockage (K,1) that would make is beneficial to insert the stent. [6 marks] e) Give two reasons why your estimates to the previous questions may not be accurate in practice? [4 marks]

Question 2 An artery has a length L and an internal diameter Dr. A build-up of plaque causes a narrowing halfway along the artery (as shown in Figure QB), which can be modelled as an obstruction with a viscous loss coefficient K₁₁. La Da Figure Q2: Flow along an artery with a obstruction (top), and flow along the same artery after a stent has been implanted (bottom). Clinicians consider performing surgery to insert a stent, which would go inside the artery and hold it open and removing the effect of the blockage, as shown in Figure Q2. The stent would have a length L, and the entry and exit to the stent would have both have a loss coefficient of K₁₂. You may assume that the flow is laminar. a) Find an expression for the pressure drop in the artery if no blockage or stent were present? [4 marks] b) Find an expression for the pressure drop after the blockage has developed? [4 marks] c) Find an expression for the pressure drop after the stent has been inserted? [7 marks] d) Clinicians will not insert stents unless they reduce the pressure drop along the artery. Find an expression for the minimum loss coefficient for the blockage (K,1) that would make is beneficial to insert the stent. [6 marks] e) Give two reasons why your estimates to the previous questions may not be accurate in practice? [4 marks]