Question 3 A team of biomedical engineer researchers develop an experiment to study the flux of fluid in capillaries. Their experimental system consists of a thin tube which has a length L and an internal diameter D = 3 mm, surrounded by a bath of distilled water. The tube is made of a semipermeable membrane which has a Staverman coefficient of σ = 0.9. The pressure at the inlet of the pipe is p₁ = 6 kPa, and the pressure at the outlet is p₂ = 1 kPa. The static pressure surrounding the tube is pp = 1 kPa. The water in the bath and the tube are both at a temperature of 28 °C, and the viscosity of water is 1 mPa.s. The ideal gas constant is 8.314 J/mol/K. a) If the researchers want a flowrate of Q = 10 ml/s, how long should the tube be? [5 marks] b) If the water in both the tube and the bath is pure (i.e. it contains no electrolytes, proteins or salts), find the variation in net filtration pressure along the tube. [5 marks] c) Researchers add NaCl to the fluid entering the tube, at a concentration of c = 1 mmol/L, find the osmotic pressure in the tube [5 marks] d) Find the variation in the net filtration pressure along the tube. Explain clearly any assumptions you make. [5 marks] e) Researchers can now add salt to the bath to adjust the flux of fluid in or out of the tube. Find the concentration of salt needed in the bath (g) for there to be no net flux of fluid across the tube. [5 marks]

Question 3 A team of biomedical engineer researchers develop an experiment to study the flux of fluid in capillaries. Their experimental system consists of a thin tube which has a length L and an internal diameter D = 3 mm, surrounded by a bath of distilled water. The tube is made of a semipermeable membrane which has a Staverman coefficient of σ = 0.9. The pressure at the inlet of the pipe is p₁ = 6 kPa, and the pressure at the outlet is p₂ = 1 kPa. The static pressure surrounding the tube is pp = 1 kPa. The water in the bath and the tube are both at a temperature of 28 °C, and the viscosity of water is 1 mPa.s. The ideal gas constant is 8.314 J/mol/K. a) If the researchers want a flowrate of Q = 10 ml/s, how long should the tube be? [5 marks] b) If the water in both the tube and the bath is pure (i.e. it contains no electrolytes, proteins or salts), find the variation in net filtration pressure along the tube. [5 marks] c) Researchers add NaCl to the fluid entering the tube, at a concentration of c = 1 mmol/L, find the osmotic pressure in the tube [5 marks] d) Find the variation in the net filtration pressure along the tube. Explain clearly any assumptions you make. [5 marks] e) Researchers can now add salt to the bath to adjust the flux of fluid in or out of the tube. Find the concentration of salt needed in the bath (g) for there to be no net flux of fluid across the tube. [5 marks]