Course Title: Fluid Mechanics Course Code: CE 2261 Credit: 3 · Course Title: Fluid Mechanics Course Code: CE 2261 Credit: 3 Book References 1. Fluid Mechanics with Engineering Application

Course Title: Fluid Mechanics

Course Code: CE 2261

Credit: 3

Book References

1. Fluid Mechanics with Engineering Application by Franzini

2. Fluid Mechanics by Streeter & Wylie

3. A Textbook of Fluid Mechanics and Hydraulic Machines by R.K. Bansal

4. 2500 solved problems in Fluid Mechanics and Hydraulics (Schaum Series) by Evett and Liu

5. Fluid Mechanics by Frank M. White

6. Fluid Mechanics Handbook by Dr. Abdul Halim (BUET)

Course Title: Fluid Mechanics

Course Code: CE 2261

Credit: 3

Syllabus Content (for 1.5 credits)

• Steady incompressible flow in pressure conduits, laminar and turbulent flow, general equation for fluid friction;

• Empirical equations for pipe flow; minor losses in pipe flow;

• Pipe flow problems-pipes in series and parallel, branching pipes, pipe networks.

Fluid Mechanics (CE 2261)

Chapter: Laminar and Turbulent Flow in Pipes

Reference: Fluid Mechanics by Dr. Abdul Halim (BUET)

Lecture prepared by

Md Nuruzzaman

Lecturer, Department of Civil Engineering

Bangladesh Army University of Engineering and Technology (BAUET)

E-mail: [email protected], [email protected]

Phone: +8801719456829

mailto:[email protected]


Laminar and Turbulent Flows in Pipes

Reynolds Number

Reynolds number is the ratio of inertia forces to viscous forces.

𝑅𝑒 =𝜌𝑉𝐷

𝜇

where, ρ is the density of fluid, V is the average velocity in the pipe, Dis pipe diameter, μ is dynamic viscosity of fluid.


State of Flow

Laminar Flow Re < 2100

Transitional Flow 2100 < Re < 4000

Turbulent Flow Re > 4000


Laminar Flow Characteristics

1. Layers of water flow over one another at different speeds withvirtually no mixing between layers.

2. The flow velocity profile for laminar flow in circular pipes isparabolic in shape, with a maximum flow in the center of thepipe and a minimum flow at the pipe walls.

3. The average flow velocity is approximately one half of themaximum velocity.


Turbulent Flow Characteristics

1. The flow is characterized by the irregular movement of particlesof the fluid.

2. The flow velocity profile for turbulent flow is fairly flat across thecenter section of a pipe and drops rapidly extremely close tothe walls.

3. The average flow velocity is approximately equal to the velocityat the center of the pipe.



Velocity profile development in a pipe







1. The region of flow near where the fluid enters the pipe is termed

the entrance (entry) region or developing flow region.

2. The fluid typically enters the pipe with a nearly uniform velocity

profile.

3. As the fluid moves through the pipe, viscous effects cause it to

stick to the pipe wall.

4. A boundary layer in which viscous effects are important is

produced along the pipe wall such that the initial velocity profile

changes with distance along the pipe, until the fluid reaches the

end of the entrance length, Once the fluid reaches the end of the

entrance region, section, the velocity profile gets constant.




Problem

Describe the state of flow of water for the following conditions:

(i) Velocity of flow = 0.19 m/s, Diameter of pipe = 0.016 m (ii)Velocity of flow = 0.0338 m/s, Diameter of pipe = 16 mm (iii)Velocity of flow = 45 cm/s, Diameter of pipe = 1.6 cm

Assume, 𝜇 = 8.94 x 10−4 kgm-1s-1.

Solution

Solve the problem using the Reynold’s number formula


Problem

An oil having kinematic viscosity of 21.4 stokes is flowing through apipe of 300 mm diameter. Determine the type of flow, if thedischarge through the pipe is 15 liters/sec.

Fluid Mechanics (CE 2261)

Chapter: Loss of Head in Pipes

Reference: Fluid Mechanics by Dr. Abdul Halim (BUET)

Lecture prepared by

Md Nuruzzaman

Lecturer, Department of Civil Engineering

Bangladesh Army University of Engineering and Technology (BAUET)

E-mail: [email protected], [email protected]

Phone: +8801719456829



Loss of Head in Pipes

Causes

The loss of head in pipes is caused by

(1) Pipe friction along the straight sections of pipe of uniform diameterand uniform roughness

(2) Changes in velocity or direction of flow.

These losses are usually referred as Major and Minor losses.


Major Losses

This is a continuous loss of head, assumed to occur at a uniform ratealong the pipe as long as the size and quality of pipe remain constant,and is commonly referred to as the loss of head due to pipe friction(hf).

Minor Losses

Minor losses consists of

1. A loss of head due to contraction of cross-section (hc).

2. A loss of head due to enlargement of cross-section (he).

3. A loss of head caused by obstructions such as gates or valves(hg).

4. A loss of head due to bends or curves in pipes (hb).


Total loss of head in a pipe, H = hf +hc +he +hg +hb

Frictional Loss in Laminar flow: Hazen-Poisuille equation


Frictional Loss with Turbulent flow: Darcy-Weisbach formula

General Laws governing fluid friction in pipes

1. Frictional loss in turbulent flow generally increases with theroughness k of the pipe.

2. Frictional loss is directly proportional to the area of the wettedsurface.

3. Frictional loss varies inversely as some power of the pipediameter.

4. Frictional loss varies as some power of the velocity.

5. Frictional loss varies as some power of the ratio of viscosity todensity of the fluid.



Combining these factors, a rational equation for loss of head due topipe friction for any fluid can be written in the form:

ℎ𝑓 = 𝐾′ × 𝑘 × 𝜋𝑑𝐿 ×1

𝑑𝑥× 𝑉𝑛 ×

𝜇

𝜌

𝑟

= 𝐾′𝑘𝜋𝜇

𝜌

𝑟×

𝐿

𝑑𝑚× 𝑉𝑛

Where K’ is a constant of proportionality and m = x = 1

The effect of viscosity and density of water on loss of head at usualflow velocities is so small that it can be neglected.



Hence, the above equation can be written as,

ℎ𝑓 = 𝐾𝐿

𝑑𝑚𝑉𝑛

Chezy proposed the value of n = 2. Darcy and Weisbach acceptedthis value and proposed the value of m = 1 and modified the equationas follows:

ℎ𝑓 = (𝐾 × 2𝑔) ×𝐿

𝑑×𝑉2

2𝑔

By substituting the friction factor ‘f’ for (K×2g), we obtain:

ℎ𝑓 = 𝑓𝐿

𝑑

𝑉2

2𝑔



The above equation is well known pipe friction formula known asDarcy-Weisbach formula.

The following equation is known as Fanning equation:

ℎ𝑓 = 4𝑓′𝐿

𝑑

𝑉2

2𝑔

Where, f = 4f’, f’ is Fanning friction factor


Limitations of Darcy-Weisbach formula

1. The loss of head with turbulent flow varies not only as the squareof the mean velocity, but as some power varying from 1.7 to 2 ormore depending on the roughness.

2. Since V = Q/A = Q/(πd2/4) for a given Q, f and L, the loss of headvaries inversely as the fifth power of diameter. Tests have shownthat the actual variation is closer to the 5.25 power and theexponent of D should be close to 1.25.

3. The friction factor should be a function of pipe roughness also,which is neglected in Darcy-Weisbach formula.


Problem

Find the loss of head due to friction in a pipe of 1 m diameter and 15km long. The velocity of water in the pipe is 1 m/s. Take f = 0.020 andneglect minor losses. Use the Darcy-Weisbach formula.

Course Title: Fluid Mechanics Course Code: CE 2261 Credit: 3 · Course Title: Fluid Mechanics Course Code: CE 2261 Credit: 3 Book References 1. Fluid Mechanics with Engineering Application

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