Frictionless flows

Adiabatic Frictionless Nozzle Flow In process plant pipelines, compressible flows are usually more nearly adiabatic than isothermal. Solutions for adiabatic flows through frictionless nozzles and in channels with constant cross section and constant friction factor are readily available. 

Example 7 Flow through Frictionless Nozzle Air at po and temperature To = 293 K discharges through a frictionless nozzle to atmospheric pressure. Compute the discharge mass flux G, the pressure, temperature, Mach mimher, and velocity at the exit. Consider two cases (1) po = 7 X 10 Pa absolute, and (2) po = 1.5 x 10 Pa absolute. 

Convergent/Divergent Nozzles (De Laval Nozzles) During frictionless adiabatic one-dimensional flow with changing cross-sectional area A the following relations are obeyed ... 

Ideal (Frictionless) Flow in Nozzles The flow path in well-formed nozzles follows smoothly along the nozzle contour without separating from the wall. The effects of small imperfections and small frictional losses are accounted for by correcting the ideal nozzle flow by an empirically determined coefficient of mscharge. The acceleration of a fluid initially at rest to flowing conditions in an ideal nozzle is given by ... 

For an irrotational, incompressible, and frictionless fluid flow there exists a scalar velocity potential 4> such that the velocity vector V is... 

Assuming steady-state, frictionless (due to the short length of the nozzles) drilling fluid flow, Equation 4-102 is written... 

In a frictionless system in which the fluid does not work on the surroundings and a and a2 are taken as unity (turbulent flow), then ... 

The mass rate of flow of a frictionless fluid between y — 5 and y = oo... 

A conical funnel is full of liquid. The diameter of the top (mouth) is Dj, that of the bottom (spout) is D2 (where D2 <time required for the fluid to drain by gravity to a level of H0/2, assuming frictionless flow. 

The adiabatic flow of an ideal gas flowing through a frictionless conduit or a constriction (such as an orifice nozzle, or valve) can be analyzed as follows. The total energy balance is... 

For an inviscid fluid, ie frictionless flow, and no pump, equation (1.10) becomes... 

It is appropriate here to define some pressure terms. Consider Bernoulli s equation for frictionless flow with no pump in the section ... 

Nitrogen contained in a large tank at a pressure P = 200000 Pa and a temperature of 300 K flows steadily under adiabatic conditions into a second tank through a converging nozzle with a throat diameter of 15 mm. The pressure in the second tank and at the throat of the nozzle is P, = 140000 Pa. Calculate the mass flow rate, M, of nitrogen assuming frictionless flow and ideal gas behaviour. Also calculate the gas speed at the nozzle and establish that the flow is subsonic. The relative molecular mass of nitrogen is 28.02 and the ratio of the specific heat capacities y is 1.39. 

In equation 8.11, which is analogous to equation 8.10, Cd is the dimensionless discharge coefficient which accounts for geometry and friction djd is the ratio of the diameter of the orifice to the inside diameter of the pipe. This ratio does not vary as does the ratio d2/dt in equation 8.10 for frictionless flow. 

Weirs are commonly used to measure the flow rate of liquids in open conduits. The theory is based on the Bernoulli equation for frictionless flow. From equation 1.13 with Ah = 0 and hf= 0... 

Equation 8.19 is based on the following assumptions the approach velocity v is uniform and parallel, the streamlines are horizontal above the weir, there is atmospheric pressure under the nappe, and the flow is frictionless. 

Liquid hehum exists in two forms, Hehum 1 and Hehum 11. The gas liquefies at 4.22°K at 1 atm to a colorless hquid known as Hehum 1. The refractive index of this hquid is 1.026, which is very close to that of the gas, thus making the surface of the hquid difficult to see. Most metal wires when placed in liquid helium or at Hehum 1 temperature exhibit superconductivity that is, frictionless flow of electrons— flow of electrical current without any resistance whatsoever. 

In order to find the relief area, it is necessary to calculate G. This will be done using Tangren et al. s method for frictionless flow, and correcting for the effects of friction using the Omega method. 

In flow through a frictionless nozzle, there is a critical pressure ratio, r, which will just cause choking. The critical pressure ratio is the ratio of the downstream back pressure to the upstream pressure, both in absolute pressure units. If the actual back pressure (e.g. atmospheric) is less than the critical pressure at which choking occurs, then there will be a pressure discontinuity at the end of the nozzle the pressure just inside the nozzle will be the critical pressure for choking, and that just outside the nozzle will be the actual back pressure, which is normally atmospheric. See Figure 9.2. -. ... 

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