Estimating The Viscosity

Bio-fluids

Bien 301

Jasma Batham

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?

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

The Problem

Required:

• To estimate the viscosity of the fluid

• To identify the fluid

The Figure

Assumptions

• Incompressible steady fluid, density is constant

• Internal flow

• Smooth pipe, no friction

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

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

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.

Calculations

fhhg

V

g

ph

g

V

g

p

2

222

1

21

22

1

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

fhhg

Vh

g

p

2

22

1 2

1

Calculations

gd

LVfh

g

Vh

g

p

22

1 22

2

22

1

Inserting the numerical values and solving for, f, we get

8.9205.0

82.317080

8.92

82.310

8.9679

700000 22

f

Therefore, f = 0.0136

Solution

Step 4

Using equation 6.38 from the book, we can now solve for the Reynolds number, where

f = 0.0136

8.0Relog21

ff

d

On calculating the value, Reynolds number =1050271.2Hence turbulent flow is confirmed

Solution

Step 4:

Now we can use the Reynolds number to calculate the viscosity

d

dV

Re

1050271

05.082.3679

Viscosity of the fluid = 0.00012 kg/ms

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.

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.

Reference

• http://www.rwc.uc.edu/koehler/biophys.2ed/fluids.html