Fluid Flow, Size Reduction, and Separation

• These study notes cover the flow of fluids, including manometers, Reynolds number, Bernoulli's theorem, energy losses, orifice meter, venturi meter, pitot tube, and rotameter.
• It also covers size reduction and separation in pharmaceutical processes.

Introduction to Fluid Flow

• A fluid is a substance that continuously deforms under applied shear stress.
• Fluids include liquids and gases.
• Fluid flow is the movement of substances that do not permanently resist distortion.
• Fluid flow studies can be divided into fluid statics and fluid dynamics.

Types of Fluids

• Ideal fluids are incompressible and have no viscosity; they are imaginary and do not exist in reality.
• Real fluids possess viscosity.
• Newtonian fluids obey Newton's law of viscosity.
• Non-Newtonian fluids do not obey Newton's law of viscosity.
• Ideal plastic fluids have shear stress proportional to the velocity gradient, with shear stress exceeding a yield value.
• Incompressible fluids maintain constant density regardless of external force.
• Compressible fluids change density with the application of external force.

Importance of Fluid Flow Understanding

• Understanding fluid flow is crucial in the manufacture of dosage forms and handling of drugs.
• The nature of fluid flow in pipes (viscous or turbulent) can be determined using the Reynolds number.

Fluid Statics (Hydrostatics)

• Fluid statics involves fluids at rest in stable equilibrium.
• There is no shear stress in fluid statics.
• Any force developed is due to pressure.
• Pressure variation is due to the weight of the liquid.
• Fluid statics studies the nature and variation of pressure at different levels when the flow rate is zero.
• A fluid exerts pressure on its surroundings.
• This pressure applies a distributed load on surfaces.
• Pressure increases with depth underwater.
• Gauge pressure is zero at the surface, regardless of the unit system used.
• The equation P = pgh relates pressure to fluid density (p), gravitational acceleration (g), and height (h).
• Principles of fluid statics are used in manometers.
• Pressure difference is measured as the difference in the heights of a liquid column.
• Fluid statics is applied in the quantification of fluid flow using Bernoulli's theorem.

Fluid Dynamics

• Fluid dynamics studies fluids in motion.
• This knowledge is important when studying liquids, gels, and ointments.
• The fluid behavior is expected to change with stress conditions.
• Mass is conserved within a control volume for constant density fluids.
• The total mass entering equals the total mass exiting the control volume.
• Its application is in calculating forces/moments on aircraft and evaluating petroleum mass flow rates.

Manometers

• Manometers measure pressure at a point by balancing a column of fluid with the same or another fluid.
• Common manometers are U-shaped tubes filled with liquid, gas, or steam.

Types of Manometers

• Simple manometers.
• Differential U-tube manometers.
• Small manometers.

Simple Manometers

• Simple manometers have a glass tube connected at one end where pressure is measured, with the other end open to the atmosphere.

Piezometer

• The piezometer measures pressure inside a vessel or pipe.
• A tube is attached to the walls of the container, allowing the liquid to rise.
• The height of the liquid rise determines pressure.

U-Tube Manometer

• The U-tube manometer consists of a glass tube bent in a V-shape.
• One end is connected to pressure at the end of a measured point, and is left open to the atmosphere.
• The tube carries mercury or another liquid.
• The mercury specific gravity is much higher than the fluid.
• Use case is measuring either gauge or vacuum pressure.

Single Column Manometer

• Consider a vertical tube micromanometer connected to a pipe containing light liquid under high pressure.
• The pressure in the pipe will force the lighter liquid in the basin to push the heavier liquid downwards.
• A slight fall of the heavy liquid level will be negligible.
• This downward movement of heavy liquid into the basin will result in a significant rise of heavy liquid in the right limb.

Inclined Tube Manometer

• The micromanometer has a tube and is inclined as shown in the figure.
• An inclined tube is more the most sensitive and called incited tube micromanometer.
• Distance moved by fluid is comparatively more
• Thus it can give a more elevated reading for a given pressure.

Differential Manometer

• Differential manometers measure the pressure difference between two points in a pipe.
• Differential manometers have a U-tube containing heavy liquid, with two ends connected by points.
• The pressure difference is measured with U-tube measurement.
• Two pieozmeters are mounted at two different gate points where the difference is to be measured.
• The differential manometer uses an inverted differential manometer.

Two Piezometer Manometer

• Consists of two piezometers mounted at two different gauge points to measure pressure difference.

U-Tube Differential Manometer

• Measures pressure difference between two points in a pipe.
• Consists of a U-shaped tube with heavy liquid.
• Both ends are connected to two desired points in a pipe.
• Differential U-tube manometers are used for measuring difference in pressure.
• The greater pressure at A will force the heavy liquid in the tube to move downwards. The downwards movement of the heavy liquid in the left will cause a rise.

Inverted Differential Manometer

• Contains a light liquid.
• They have their two ends connected to the point whos pressure differnec is to be measures.
• Used for measuring the difference in low pressure.
• The figure shows that an inverter U-Tube is a manometer connected to two points A and B.

Small Manometer

• The type of manometer works based on principle of an inclined tube mometer
• small manometers or pressure gauages measure the very small preosure variations.
• Modified variant of a simple manometer whos part its formed by as large cross-sectional
• Highly precise instrument capable of observing very small perssure variations with high accuracy.

Advantages of Manometers

• Simple to construct.
• Great accuracy.
• Used to measure pressure, temperature, flow and other process variables.
• Low cost.
• Better sensitivity.

Disadvantages of Manometers

• Has smaller dynamic response.
• Fragile, low portability.
• Small operational limits which are on the order of 1000 kN/m2.
• Density is dependent on temperature.

Applications of Manometers

• Maintenance of heating, ventilation, and air conditioning (HVAC) systems and gas systems.
• Constructing bridges, swimming pools, and other engineering purposes.
• Climate forecasting.
• Clinical applications such as blood pressure measuring and physiotherapy.

Reynolds Number

• In Reynolds experiment, the flow conditions are affected by four factors: diameter of pipe (D), average velocity (u), density of liquid (p), and viscosity of the fluid (η).

• Reynolds number is grouped into an expression as given below, Re = Dup/η

• Inertial forces are due to mass and the velocity of the fluid particles tyring to diffuse the fluid practicles.

• Voscous force if the fractoral force due to the viscosity of the fluid whichh makes the motion of the fluid parallel.

• Types of Flow

• Types of flow is laminar flow It is when the fluid partivcles move in layers or laminar with one later sliding with another.

• Turbulent flow

  It is when velocity of the water is increased the thread of the water is increased. Solution and the fluid in the fliud is turbulent flow.

  Velocity is when the velfocity and criticial velocuty laminar flow to turbulent.

Laminar Flow

• Fluid particles move in layers that slide with each other.
• No exchange of fluid particles occurs between layers.
• If Re < 2000, the flow is laminar.

Turbulent Flow

• Turbulent flow occurs when the velocity of the water is increased the thread of the water is increased.

Applications of Reynolds Number

• Predicting the nature of flow in a set of conditions.
• Studying particle sedimentation (Stokes' law).
• The rate of heat transfer in liquids depends on the type of flow (viscous/turbulent).
• Reynolds number is a factor for purified water distribution.
• Reynolds number maintains the required flow and prevented by the formation of biofilm.

Bernoulli's Theorem

• A fluid in motion is subjected to several forces.
• The variations in the acceleration and energies in flow phenomenon.

Principle of Benoulli's Thoereom.

When the principle of conservedation of energy is followed from fliuds. Result ing equation is called Benoullois Therm. Pumps generally supply energy for concecung liquide form one point to another.

Bernoulli's Theorem Total Energy Expression

• It is based on pressure energy, kinetic energy, and datum energy.

Energy balance

Energy balance equals point A and B can be accounted the equation such as energy may be read as equation Eqiations is calle Beraoullies Equation a

Losses in fittings

• when fitiings are introducted into a Straght Pipe. That will cause disturbance s in the flow Its difficult to specify losses due to the type cause its vary fitting type.

Losses in Fittitngs.

direction change for example elbow fittings type

• Change in the tube type 3 Enlargeements losses. cross ection of ythe pipe enalarges gradually and adapt to a change

4 losses from contraction

Orifice meeter

An device with hose measured Recording prressure decrease accross the hole

5 prinviples

• It will rediuce the crass sectrional. Arear
• pressure
• pressure different

Advantages

• The orrifice meters iis very compared
• It can be vertical horizontal and incilitated It requires a straight pipe for better accry. 1 is more cheap

Disadvantages

Linitation to the cova contral length for reading the flow is some time.

• its single pase of the fluid .

Flow losses

• If energy is transformer, more from one place their always enegry losse
• Potentaiaalityy results to and friction an And drag _ heat

Priciples

 Bernoulli's equation includes the term "loss of energ" in the pipe

• According to the conservatance, balances have proper beaccouner
• There for is nessavrt to calculate the energy losses fluids experience energy losses is while flowing
• *TYPES OF ENGERYY LOSSES

friction 2 enger y losses into fittings

3 energy from enlagernt losses

Venteriemnters

• type of meter that Bernoulli's Equation