This document discusses basic equations of fluid mechanics used in a biofluid mechanics and heat transfer course. It covers the Bernoulli equation and its application to problems involving blood flow in the aorta and capillaries. It also discusses venturi meters, which use the Bernoulli principle to measure fluid flow rates. Venturi meters have a constricted section that causes velocity and pressure to change in a way that can be used to calculate flow rates. The document provides equations for calculating theoretical discharge through a venturi meter and defines related terms like cross-sectional area and velocity at different pipe sections.

1. Biofluid Mechanics and Heat Transfer
Course Code: 04041115
Lecture 06: Basic Equations of Fluid Mechanics
Date: 31/07/2023
Course Teacher: Tohfatul Jinan
Lecturer
Department of Biomedical Engineering BUHS
BANGLADESH UNIVERSITY OF HEALTH SCIENCES
Department of Biomedical Engineering
1

2. 2
Bernoulli Equation

3. 3

4. 4
Problem 1

5. 5

6. 6
Problem 2

7. 7

8. Problem-3
8
In an adult, the aorta's radius is normally 1.5cm,
and blood moves through it at an average
speed of 30cm/s. If the typical capillary has a
radius of 5 x 10-6 m, and blood passes through
them with a velocity of 0.1cm/s, approximately
how many capillaries are in the body?
Determine the mass flow rate of blood in the
capillaries and aorta if the blood density is 1060
kg/m??(HW)

9. 9
Venturi Meters
● Venturi meters are used to measures the flow rate of a
fluid through a pipe. This is an application of
Bernoulli’s equation.
● Venturi meter theory works on the Bernoulli equation
such that the velocity increases as the pressure
decreases.
● This theory states that when the cross-sectional area
of the flow decreases, a pressure difference between
the different regions of the flow is created, and it helps
to measure the difference under pressure.
● This pressure differential helps to measure the
discharge inflow

10. Venturi effect
10
The Venturi effect is the reduction in fluid pressure that results when a fluid flows through
a constricted section (or choke) of a pipe.

11. Venturi masks
11
Venturi masks are low-flow masks
that use the Bernoulli principle to
entrain room air when pure oxygen
is delivered through a small orifice,
resulting in a large total flow at
predictable Fio2.

12. 12

13. HW
13
1. Principle of venturi mask
2. Difference between venturi mask and oxygen mask

14. The Expression for the Rate of Flow-Through Venturimeter:
14
Let,
a1 = cross-section area of the inlet pipe
d1 = diameter of the inlet pipe
v1 = velocity at the inlet pipe
p1 = pressure at the inlet pipe
also,
a2 = cross-section area of the throat
d2 = diameter of the throat
v2 = velocity at the throat
p2 = pressure at inlet throat

15. 15
d1, p1, v1, and a1 are the diameters at the inlet, the pressure at the inlet, the velocity at
the inlet, and the area at cross-section 1.
And d2, p2, v2, and a2 are the corresponding values in section 2.
Applying Bernoulli’s equations in sections 1 and 2:
As the pipe is Horizontals, so z1 = z2
Therefore (P1 – P2)/ρg is the difference of pressure heads at sections 1 and
2, and it is equal to h. so

16. 16
Substituting these values of h in equation (1), we get
Now applying continuity equations at section 1 and 2
Substituting this value of v1 in equations (2) and solving, we get

17. 17
Discharge
Substitutions the value of v2 in the above equation
Q is the theoretical discharges under ideal conditions. The actual discharge will be less than the
theoretical discharge. The actual discharges are given by the formula.
Where Cd is the coefficients of the venturimeter, and its value is less than 1.

18. 18
Home Study
Reference:
https://mechanicaljungle.com/working-of-venturimeter/
1. Advantages of Venturimeter
2. Disadvantages of Venturimeter
3. Applications of Venturimeter

19. 19
Hagen Poiseuille Equation

20. 20

21. Biofluid Mechanics and Heat Transfer :
BANGLADESH UNIVERSITY OF HEALTH SCIENCE
BIOMEDICAL ENGINEERING
21
Thank you!