70. Write differential form of continuity equation for steady flow and call its members.

 The continuity equation states that, in any steady state process, the rate at which mass enters a system is equal to the rate at which mass leaves the system.

The differential form of the continuity equation is:

where

ρ is fluid density,

t is time,

u is the flow velocity vector field.

In this context, this equation is also one of Euler equations. The Navier-Stokes equations form a vector continuity equation describing the conservation of linear momentum.

Steady flow

70. Write differential form of continuity equation for incompressible flow and call its members.

The differential form of the continuity equation is:[1]

where

ρ is fluid density,

t is time,

u is the flow velocity vector field If ρ is a constant, as in the case of incompressible flow, the mass continuity equation simplifies to a volume continuity equation:[1]

which means that the divergence of velocity field is zero everywhere. Physically, this is equivalent to saying that the local volume dilation rate is zero.

70. W rite continuity equation for infinitesimal stream tube, one dimensional flow with finite cross section area and call its members.

Where A – is a cross-section area

This equation is general continuity equation for one dimensional flow.

70. Which physical values are considered as gas state parameters?

Parameter 1: Temperature

Temperature (T) is an indicator of the average kinetic energy that a sample of matter possesses. If a sample could be viewed nanoscopically (on a scale of 10^-9 meters), its constituent particles would be observed to be in constant motion. The nature of these motions would become increasingly disordered as the state of matter varies- solids would undergo a more harmonic, organized motion, gases a completely chaotic motion, and liquids somewhere in between. A "hot" body would be observed to have more of this kinetic motion than a "cooler" body. If two systems are able to exchange energy of motion (a condition called thermal contact), a faster-moving body would naturally transfer momentum to a slower-moving body. The rate and magnitude of this transfer depends on the bonding relationships which macroscopically act as the heat capacity of matter, allowing some materials to heat or cool more dramatically than others. Energy continues to flow from hot to cold until the two bodies reach thermal equilibrium, where momentum is equally transferred between the two. The bodies are then said to be at the same temperature. To assign temperature, we place a body in thermal contact and allow it to come to thermal equilibrium with a device called a thermometer. Traditionally a liquid (typically mercury or alcohol) with known coefficient of expansion is used as a thermometer. Heating expands and cooling contracts the liquid, and these processes can be calibrated to one of the accepted temperature scales. A digital thermometer passes a fixed current through a metal probe. The probe has a temperature-dependent change in resistance, so resulting output voltage accurately measures the temperature of a system.

Parameter 2: Pressure

Pressure (the symbol: p) is the ratio of force to the area over which that force is distributed.

Pressure is force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure (also spelled gage pressure)^[a] is the pressure relative to the local atmospheric or ambient pressure. While pressure may be measured in any unit of force divided by any unit of area, the SI unit of pressure (the newton per square metre) is called the pascal (Pa) after the seventeenth-century philosopher and scientist Blaise Pascal. A pressure of 1 Pa is small; it approximately equals the pressure exerted by a dollar bill resting flat on a table. Everyday pressures are often stated in kilopascals (1 kPa = 1000 Pa).

Fluid pressure is the pressure at some point within a fluid, such as water or air (for more information specifically about liquid pressure, see section below).

Fluid pressure occurs in one of two situations:

1. an open condition, called "open channel flow"

   1. the ocean, or

   2. swimming pool, or

   3. the atmosphere.

2. a closed condition, called closed conduits

   1. water line, or

   2. gas line.

Parameter 3: Density

The density of air, ρ (Greek: rho) (air density), is the mass per unit volume of Earth's atmosphere, and is a useful value in aeronautics and other sciences. Air density decreases with increasing altitude, as does air pressure. It also changes with variances in temperature or humidity. At sea level and at 15 °C according to ISA (International Standard Atmosphere), air has a density of approximately 1.225 kg/m³ (0.0023769 slugs/ft³).