Liquid Flow ```In most flows of liquids, and of gases at low Mach number, the mass density of a fluid parcel can be considered to be constant, regardless of pressure variations in the flow. For this reason the fluid in such flows can be considered to be incompressible and these flows can be described as incompressible flow. Bernoulli performed his experiments on liquids and his equation in its original form is valid only for incompressible flow. A common form of Bernoulli's equation, valid at any arbitrary point along a streamline where gravity is constant, is: Bernoulli's equation is usually written as (v²/2) + gz + p/ρ = constant v is the fluid flow speed at a point on a streamline, g is the acceleration due to gravity, z is the elevation of the point above a reference plane, with the positive z-direction pointing upward – so in the direction opposite to the gravitational acceleration, p is the pressure at the chosen point, and ρ is the density of the fluid at all points in the fluid. alternate forms ½ρv² + ρgz + p = constant ½v² + gz + p/ρ = constant Simplified form In many applications of Bernoulli's equation, the change in the ρ g z term along the streamline is so small compared with the other terms it can be ignored. For example, in the case of aircraft in flight, the change in height z along a streamline is so small the ρ g z term can be omitted. This allows the above equation to be presented in the following simplified form: p + q = p₀ where p is the pressure at the chosen point, and p₀ is total pressure, and q is dynamic pressure. or static pressure + dynamic pressure = total pressure Reynolds number Re = ρuL/μ = uL/v Re is Reynolds number ρ is the density of the fluid (SI units: kg/m³) u is the velocity of the fluid with respect to the object (m/s) L is a characteristic linear dimension (m) μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/m·s) ν is the kinematic viscosity of the fluid (m²/s). The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface. These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension (L in the above equation). This dimension is a matter of convention – for example radius and diameter are equally valid to describe spheres or circles, but one is chosen by convention. For aircraft or ships, the length or width can be used. For flow in a pipe, or for a sphere moving in a fluid, the internal diameter is generally used today. Other shapes such as rectangular pipes or non-spherical objects have an equivalent diameter defined. For fluids of variable density such as compressible gases or fluids of variable viscosity such as non-Newtonian fluids, special rules apply. The velocity may also be a matter of convention in some circumstances, notably stirred vessels. ``` Home Area, Volume Atomic Mass Black Body Radiation Boolean Algebra Calculus Capacitor Center of Mass Carnot Cycle Charge Chemistry   Elements   Reactions Circuits Complex numbers Constants Curves, lines deciBell Density Electronics Elements Flow in fluids Fourier's Law Gases Gravitation Greek Alphabet Horizon Distance Interest Magnetics Math   Trig Math, complex Maxwell's Eq's Motion Newton's Laws Octal/Hex Codes Orbital Mechanics Particles Parts, Analog IC   Digital IC   Discrete Pendulum Planets Pressure Prime Numbers Questions Radiation Refraction Relativistic Motion Resistance, Resistivity Rotation Series SI (metric) prefixes Skin Effect Specific Heat Springs Stellar magnitude Thermal Thermal Conductivity Thermal Expansion Thermodynamics Trigonometry Units, Conversions Vectors Volume, Area Water Wave Motion Wire, Cu   Al   metric Young's Modulus