64 Quality change flow parameters when it pass shock wave.
As an object moves through a gas, the gas molecules are deflected around the object. If the speed of the object is much less than the speed of sound of the gas, the density of the gas remains constant and the flow of gas can be described by conserving momentum, and energy. As the speed of the object approaches the speed of sound, we must considercompressibility effects on the gas. The density of the gas varies locally as the gas is compressed by the object.
For compressible flows with little or small flow turning, the flow process is reversible and the entropy is constant. The change in flow properties are then given by the isentropic relations . But when an object moves faster than the speed of sound, and there is an abrupt decrease in the flow area, shock waves are generated in the flow. Shock waves are very small regions in the gas where the gas properties change by a large amount. Across a shock wave, the static pressure, temperature, and gas density increases almost instantaneously. The changes in the flow properties are irreversible and the entropy of the entire system increases. Because a shock wave does no work, and there is no heat addition, the total enthalpy and the total temperature are constant. But because the flow is non-isentropic, the total pressure downstream of the shock is always less than the total pressure upstream of the shock. There is a loss of total pressure associated with a shock wave.
65 Write expression for calculation mass flow rate through infinitesimal surface.
The surface integral of the (continuous) function f(x, y, z) over the surface S is denoted by
can
think of dS as the area of an infinitesimal piece of the surface S.
To define the integral , we subdivide the surface
into small pieces having area ∆Si, pick a point (xi, yi, zi) in the
i-th piece, and form the Riemann sum:
Write the formula for calculation the divergence of the vector in orthogonal coordinate system.
Formulate mass conservation principle.
principle of mass conservation, states that for any system closed to all transfers of matter and energy (both of which have mass), the mass of the system must remain constant over time, as system mass cannot change quantity if it is not added or removed., The quantity of mass is "conserved" over time.
