Flow of Fluids, Pharmaceutical Engineering, B.Pharmacy As per PCI Syllabi

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.

Part 1:

Manometers:

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 P₁ Pascal's and point 5 will be P₂ Pascal's

THe pressure at point 2 can be wirtten as

=P₁ + (m + R)ρ_Bg 

Since  ΔP =  Δ hρg
(m+R) = distance from 3 to 5.
Since the points 2 nad 3 are at same height the pressure.

Pressure at 3 =  P₁+ (m + R)ρ_Bg

Pressure at 4 is less than pressure ar point 3 by Rρ_Ag.

Pressure at 5 is still less thatn pressure point 4 by mρ_Bg.

Form all above equations:

P₁ + (m + R)ρ_Bg - Rρ_Ag - mρ_Bg =  P₂ 

ΔP = P₁ - P₂ = 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.

• Diffenrential manometers find occasional application. 
• This is suitable for measurement of small pressure differences.
• Sensitive device and useful for measuring even small gas pressure.

Pressure at 

Point 1 = P₁

Point 2 = P_{1 +} aρ_Bg / g_c 

Point 3 = P_1 + aρ_Bg / g_c + bρ_Ag / g_c
Point 4 = P_1 + aρ_Bg / g_c + bρ_Ag / g_c 

Point 5 = P_1 + aρ_Bg / g_c + bρ_Ag / g_c  - Rρ_Cg / g_c

Point 6 = P_1 + aρ_Bg / g_c +  bρ_Ag / g_c  - Rρ_Cg / g_c - dρ_Ag / g_c

Point 7 = P_1 + aρ_Bg / g_c +  bρ_Ag / g_c  - Rρ_Cg / g_c - dρ_Ag / g_c - aρ_Bg / g_c = P₂

The last equation may simplified to

P1 - P2 = (d - b)ρ_Ag / g_c+  Rρ_Cg / g_c

_{but since b - d = R, or fd - b = -R,}

ΔP = P₁ - P₂ = R( ρ_C - ρ_A)g / g_c

Hence smaller the difference between ρ_C and ρ_A larger will be R.

Applications:

• 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.