1. Estimating The Viscosity Bio-fluids Bien 301 Jasma Batham

2. The Problem In the given figure, suppose p1= 700KPa and the fluid specific gravity is 0.68. If the flow rate is 27m^3/h, estimate the viscosity of the fluid. What fluid in table A.3 is the likely suspect?

3. The Problem Given: P1, pressure in the tank = 700KPa Specific gravity of the fluid = 0.68 Q, flow rate of the fluid = 27m^3/h

4. The Problem Required: To estimate the viscosity of the fluid To identify the fluid

5. The Figure

6. Assumptions Incompressible steady fluid, density is constant Internal flow Smooth pipe, no friction

7. Solution Step1: Since we know the flow rate, Q = 27m^3/h, and the diameter of the pipe, d = 5cm, we can calculate the Velocity. V = Q/ A = Q/ (πd^2/4) = 27/3600 ((3.14* (0.05^2))/4) = 3.82m/s

8. Solution Step 2 Next we can calculate the density of the fluid, using specific gravity = 0.68 and density of the water =998kg/m^3. ρ =0.68* 998 kg/m^3 = 679Kg/m^3

9. Solution Step 3 Next applying the steady flow energy equation between point 1 and 2, we can find the Darcy’s friction, f. p1 =700kpa, p2 = 0, V1 = 0, V2=3.82, d = 0.05m, h1=10m, h2 = 80m, L = 170m (length of the pipe), α = can be neglected.

10. Calculations After taking into consideration the points from the previous slide, the above equation reduces down to the following equation.

11. Calculations Inserting the numerical values and solving for, f, we get Therefore, f = 0.0136

12. Solution Step 4 Using equation 6.38 from the book, we can now solve for the Reynolds number, where f = 0.0136 On calculating the value, Reynolds number =1050271.2 Hence turbulent flow is confirmed

13. Solution Step 4: Now we can use the Reynolds number to calculate the viscosity Viscosity of the fluid = 0.00012 kg/ms

14. Conclusion Using the table A.3, we compare the calculated viscosity and density with those in the table and the closest we got to was gasoline. Therefore the mystery fluid is Gasoline.

15. Biomedical Application In the human body,the blood is constantly moving. The viscosity of the blood is not necessarily the same at any two given points. The viscosity of the blood changes with respect to its velocity as blood is not an uniform fluid, thus the concept of this problem can be used to calculate the blood viscosity at a given point.

16. Reference http://www.rwc.uc.edu/koehler/biophys.2e d/fluids.html