Flow through a converging nozzle

The pressure drop P along a tube of length L that reduces in radius from ai to for a power-law liquid at a flow-rate Qis given by 

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Pressure profiles for compressible flow through a convergent nozzle... 

Section 5.6 shows a comparison of the velocities for flow through a converging nozzle, calculated by means of (a) Bernoulli s equation, assuming that air was a constant-density fluid, and (b) the equations for isentropic flow. Show the calculations in the latter case, and check your answers against those shown in Sec. 5 6. 

By feeding the mixture through a converging nozzle, the velocity profile may be made nearly flat or uniform. A Bunsen flame in such a flow has a smaller range of stabiUty but the mechanism is essentially the same and the flame very closely approximates a cone. If the apex angle of the flame is , then S can be obtained from equation 21... 

A practical example of flow through a converging-diverging nozzle is given in Example 4.4... 

Air is fed from a reservoir through a converging nozzle into a 1 /2 in. ID drawn steel tube that is 15 ft long. The flow in the tube is adiabatic, and the reservoir temperature and pressure are 70°F and lOOpsia. 

The case of flow through a convergent-divergent nozzle is shown in Figure 6.2. On reducing the back pressure PB, while keeping the supply... 

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. 

Consider the case in which an ideal gas flows from one tank to another tank at a lower pressure through a convergent nozzle. The second tank is assumed to be at a constant pressure. The flow may be assumed to be isentropic so that the mass flow rate is given by equation 6.107. 

Air at a pressure of 5 bar in a closed tank is to be vented by allowing it to discharge through a convergent nozzle straight to the atmosphere. Show that the mass flow rate M is given by... 

For example, T /T0 = 0.833, p /po = 0.528, and p /po = 0.634 are obtained when y = 1.4. The temperature T0 at the stagnation condition decreases 17 % and the pressure p0 decreases 50% at the nozzle throat. The pressure decrease is more rapid than the temperature decrease when the flow expands through a convergent nozzle. The maximum flow velocity is obtained at the exit of the divergent part of the nozzle. When the pressure at the nozzle exit is vacuum, the maximum velocity is obtained by the use of Eqs. (1.48) and (1.6) as... 

Hence equation (14.63) for mass flow through a convergent-only nozzle becomes ... 

The area-velocity relation provides important insight regarding the behavior of a quasi-ID compressible flow in a channel of varying cross section. It states that for a subsonic flow (M < 1) to increase velocity, a decrease in cross-sectional area is required. This is an intuitive and familiar result similar to incompressible flow theory. In contrast, acceleration of a supersonic flow (M > 1), requires an increase in area a counter-intuitive result when viewed from an incompressible flow perspective. This relation also indicates that sonic velocity (M = 1) can only occur at a nozzle throat where the area is a minimum. It thus follows for a gas to expand from subsonic to supersonic velocities, it must flow through a convergent-divergent channel arrangement. 

If the back pressure is reduced below P, there is no increase in the flow rate through the nozzle, ie the flow is choked. In a convergent nozzle it is impossible for the gas speed to exceed the speed of sound. This case is... 

Air flows from a large reservoir where the temperature and pressure are 25°C and 10 atm, through a convergent-divergent nozzle and discharges to the atmosphere. The area of the nozzle s exit is twice that of its throat. Show that under these conditions a shock wave must occur, (y = 1.4.)... 

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