Answer to Question #176778 in Physics for Praise

Question

A patient is given sucrose intravenously. Her venous pressure is 18mmHg, and the elevation difference between the intravenous needle and sucrose bottle is 0.80m. If the rate of sucrose flow is to be 2.0mL/min, what should the diameter of the 4.0 cm long needle be? Assume the sucrose has the same viscosity and density as blood

Answer 1

$$\rho gh=p_1+\frac{8Q\eta L}{\pi r^4}\\ \rho gh=p_1+\frac{Q\eta L}{2\pi d^4}\\ \\ (1050)(9.8)(0.8)=2400+\frac{(3.33\cdot10^{-8})(0.004)(0.04)}{2\pi d^4}\\d=0.11\ mm$$