Fluid Mechanics Lecture

Fluid mechanics is a core subject in civil and mechanical engineering, dealing with the study and behavior of fluids (gases and liquids). Fluids are defined as any substance that can flow, encompassing both liquids and gases. The field is divided into fluid statics (fluids at rest) and fluid dynamics (fluids in motion).

Density (ρ) is defined as mass per unit volume (m/V) and its SI unit is kg/m³. Homogeneous materials have the same density regardless of size or shape. Density is a crucial factor in determining whether an object will sink or float. For example, water's density is 1 x 10³ kg/m³.

This section includes an example problem: calculating the mass and weight of air in a living room (4m x 5m x 3m). Using the density of air (1.2 kg/m³) and the room's volume, the mass is found to be 72 kg, and the weight is 706.32 Newtons.

Pressure is defined as the force exerted per unit area (P = F/A), with the force acting perpendicularly to the surface. The SI unit for pressure is Pascal (Pa), equivalent to 1 Newton per square meter (N/m²). Pressure increases when force increases or when the area over which the force is applied decreases. Practical examples include the pain from high heels (small area, high pressure) and ear pressure in elevators or while diving (pressure as a function of height).

Pressure also varies with depth, given by the formula P = ρgh, where ρ is fluid density, g is acceleration due to gravity, and h is height/depth. This explains why pressure increases as one goes deeper underwater or higher in elevation. For open tanks, atmospheric pressure (P_atm ≈ 101.3 kPa) must be added to the ρgh calculation.

A problem demonstrates calculating total pressure at the bottom of a 3-meter deep swimming pool, comparing fresh water and seawater. Seawater, with a slightly higher density, results in greater pressure (132.12 kPa for seawater vs. 130.73 kPa for fresh water).

Common pressure units include Pascal (Pa), bar (1 bar = 0.1 MPa), atmospheres (1 atm = 101.325 kPa), and millimeters of mercury (mmHg). One Torr is approximately equal to 1 mmHg.

Pascal's principle states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the container. This principle is fundamental to hydraulic systems, where a small force over a small area can generate a large force over a large area (P1 = P2, or F1/A1 = F2/A2).

Two example problems illustrate Pascal's principle using hydraulic presses. The first shows how a small force (25 Newtons) on a 5 cm radius piston can lift a 10 kiloNewton car on a 1-meter radius piston. The second calculates the force and pressure needed to lift a 13,300 Newton car using pistons with 5 cm and 15 cm radii.

The derivation of hydrostatic pressure (ΔP = ρgΔh) is presented, showing how pressure changes with depth by analyzing forces on a small cubic element of fluid at rest. This derivation confirms the direct relationship between pressure change and height change within a fluid.

Buoyant force is the upward force exerted by a fluid on an immersed object. Archimedes' principle states that the magnitude of this buoyant force is equal to the weight of the fluid displaced by the object. The determining factor for an object to float or sink is its density relative to the fluid's density: if object density < fluid density, it floats; if object density > fluid density, it sinks.

Bernoulli's equation describes the conservation of energy in moving fluids, relating pressure, fluid velocity, and height (P + ½ρV² + ρgh = constant). The continuity equation (A1V1 = A2V2) states that for an incompressible fluid, the mass flow rate is constant through a pipe, even when the cross-sectional area changes.

A problem demonstrates how to use the continuity equation and Bernoulli's equation to find the speed and pressure of gasoline flowing through a pipe with changing diameter and height. Given initial conditions, the final velocity and pressure are calculated.