Principles of Fluid Mechanics and Particle Size Reduction
Fluid Mechanics Fundamentals
A fluid is a substance that continually deforms (flows) under an applied shear stress.
Types of Fluids
- Ideal fluid: An imaginary, incompressible fluid with zero viscosity that does not exist in reality.
- Real fluid: All fluids that possess viscosity.
- Newtonian fluid: Fluids that obey Newton’s law of viscosity.
- Non-Newtonian fluid: Fluids that do not obey Newton’s law of viscosity.
- Ideal plastic fluid: Fluids where shear stress is proportional to the velocity gradient, provided shear stress exceeds the yield value.
Fluid Statics
Also known as Hydrostatics. When a fluid is at rest in stable equilibrium, there is no shear stress. Any force developed is due to pressure, and pressure variation is simply due to the weight of the liquid. In fluid statics, we study the nature of pressure exerted by a fluid and its variation at different levels when the flow rate is zero.
Principles of Fluid Statics
A fluid, like water or air, exerts pressure on its surroundings, applying a distributed load on surfaces such as dams, irrigation gates, or steam boilers.
Formula: P = ρgh, where ρ is the density, g is gravitational acceleration, and h is the height of the fluid above the point of interest.
Applications
Fluid statics principles are employed in manometers to measure pressure differences and in Bernoulli’s theorem for quantifying fluid flow.
Fluid Dynamics
Fluid dynamics deals with the study of fluids in motion. This knowledge is essential for liquids, gels, and ointments that change flow behavior under different stress conditions.
Principle: Conservation of Mass
Basic fluid mechanics laws dictate that mass is conserved within a control volume for constant density fluids. The total mass entering must equal the total mass exiting.
Applications
- Calculating forces and moments on aircraft.
- Determining mass flow rates of petroleum through pipelines.
- Predicting weather patterns.
Manometers
A manometer is a device used to measure pressure at a point in a fluid by balancing the column of fluid. It is commonly a U-shaped tube filled with liquid, gas, or steam.
Types of Manometers
- Simple Manometer: A glass tube with one end connected to the pressure source and the other open to the atmosphere.
- Piezometer: A tube attached to the walls of a vessel or pipe to measure internal liquid pressure.
- U-tube Manometer: A V-shaped glass tube used to measure pressure relative to the atmosphere.
- Differential Manometer: A U-tube containing a heavy liquid used to measure the pressure difference between two points.
Applications
- Maintenance of HVAC and gas systems.
- Construction of bridges and swimming pools.
- Climate forecasting.
- Clinical applications like blood pressure measurement.
Reynolds Number
In Reynolds’ experiment, flow conditions are affected by pipe diameter (D), average velocity (u), density (ρ), and viscosity (η). These are grouped into the Reynolds number (Re): Re = (ρuD) / η.
Types of Flow
- Laminar flow: Fluid particles move in layers with no exchange between layers (Re < 2000).
- Turbulent flow: Complete mixing occurs, and the flow is uniformly colored (Re > 4000).
Bernoulli’s Theorem
When the principle of conservation of energy is applied to fluid flow, the resulting equation is Bernoulli’s theorem. It is applied in the measurement of flow rates using orifice meters, venturi meters, and the operation of centrifugal pumps.
Venturimeter
A venturimeter is a flowmeter that works on the principle of Bernoulli’s equation. It consists of two tapered sections inserted into a pipeline to measure flow rate by creating a pressure drop at a narrow throat.
Pitot Tube
A pitot tube measures fluid flow velocity. A tube at right angles to the flow measures pressure head only, while a tube pointing upstream measures both pressure head and velocity head.
Rotameter
A rotameter measures the volumetric flow rate of fluid in a closed tube. It is a variable-area flowmeter where a plummet rises and falls within a tapered tube based on the flow rate.
Size Reduction Processes
Advantages of Size Reduction
- Content Uniformity: Small, uniform particles ensure effective mixing.
- Uniform Flow: Controlled particle size promotes consistent flow into dies during tablet compression.
Theories of Size Reduction
- Rittinger’s Theory: Energy required is directly proportional to the new surface area produced.
- Bond’s Theory: Energy used in crack propagation is proportional to the new crack length produced.
- Kick’s Theory: Energy used is proportional to the ratio of size changes.
Milling Equipment
- Hammer Mill: Reduces particle size by impact with rapidly moving hammers (8,000 to 15,000 RPM).
- Ball Mill: A rotating drum containing pebbles or metal balls that grind material via impact.
- Edge Runner Mill: Uses heavy steel rolls or grindstones to crush material through compression and shearing forces.