## Flow of Fluids

### Content: Types of manometers, Reynolds numbers and its significance, Bernoulli's theorem and its applications. Energy losses, Orifice meter, Venturimeter, Pitot tube and Rotameter.

Part 1:- Types of manometers

Part 2:- Reynolds numbers and its significance

Part 3:- Bernoulli's theorem and its applications

Part 4:- Energy losses, Orifice meter, Venturimeter, Pitot tube and Rotameter.

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__Part 1:__

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__Manometers:
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Manometers are the devics used for measuring the pressure differences. Pressure differences based on the principle of balancing the column of liwud by the same or another column of liquids. Three different manometes are available are:

1. Simple Manometes

2. Differential Manometers

3. Inclined Manometers

### Principles and Applications of Manometers:

### Simple Manometers

Simple manometers is a device which measures pressure at a point in a fluid contained pipe or vessel.

- Most commonly used manometer
- it consists of a glass U shaped tube filled with a liquid A of density ρ
_{A}kg /meter cude and above A the arms are filled with liquid B of density ρ_{B}. - The liquid A and B are immiscible and the interface can be seen clearly.
- If two different pressures are applied on the two arms the meniscus on the one liquid will be higher than the other.
- Let pressure at point 1 will be P
_{1}Pascal's and point 5 will be P_{2}Pascal's

=P

Since ΔP = Δ hρg_{1}+ (m + R)ρ_{B}g(m+R) = distance from 3 to 5.

Since the points 2 nad 3 are at same height the pressure.

Pressure at 3 = P

_{1}+ (m + R)ρ_{B}g
Pressure at 4 is less than pressure ar point 3 by Rρ

_{A}g.
Pressure at 5 is still less thatn pressure point 4 by mρ

_{B}g.
Form all above equations:

P

_{1}+ (m + R)ρ_{B}g - Rρ_{A}g - mρ_{B}g = P_{2 }
ΔP = P

_{1 }- P_{2}= R( ρ_{A}- ρ_{B})g#### Applications:

- Pressure difference can be determined by measuring R.
- Manometer are use in measuring flow of fluid.
- Simple Manometer helps in measuring the consumption of gases in the chemical reactions.
- Manometers are used in conjuction with flow meters for the measurement of flow of fluids. For example, Venturi meter and orifice meter are used for the measurment of pressure head using a manometer. Pitot tube measure the velocity head using manometer.

### Differential Manometers

Differential Manometer is manometer which measure the difference of pressure between any two points in a pipe or vessel containing fluid.

Point 2 = P

_{1 +}aρ_{B}g / g_{c}
Point 3 = P

Point 4 = P

_{1}_{ +}aρ_{B}g / g_{c}+ bρ_{A}g / g_{c}Point 4 = P

_{1}_{ +}aρ_{B}g / g_{c}+ bρ_{A}g / g_{c}
Point 5 = P

_{1}_{ +}aρ_{B}g / g_{c}+ bρ_{A}g / g_{c}- Rρ_{C}g / g_{c}
Point 6 = P

_{1}_{ +}aρ_{B}g / g_{c}+ bρ_{A}g / g_{c}- Rρ_{C}g / g_{c}- dρ_{A}g / g_{c}
Point 7 = P

The last equation may simplified to

_{1}_{ +}aρ_{B}g / g_{c}+ bρ_{A}g / g_{c}- Rρ_{C}g / g_{c}- dρ_{A}g / g_{c}- aρ_{B}g / g_{c }= P_{2}The last equation may simplified to

P1 - P2 = (d - b)ρ

_{A}g / g_{c}+ Rρ_{C}g / g_{c}_{but since b - d = R, or fd - b = -R,}

ΔP = P

_{1 }- P_{2}= R( ρ_{C}- ρ_{A})g / g_{c}
Hence smaller the difference between ρ

Applications:_{C}and ρ_{A }larger will be R.- Micromanometers based on the liquid column principle are available commercially.
- It measure the reading with extreme precision and sensitivity.
- These are free from errors due to capillary and require no calibration, apart from checking the micrometer scale.

### Inclined Tube Manometers

Inclined Tube Manometers or Inclined Manometers is a manometer which measures the minute pressure differences between any two points in a fluid contained in a pipe or vessel.

- To measure small pressure differences need ot magnify R
_{m}, some way.

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