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Consider a supersonic flow with given a stagnation pressure po, and stationary shock of arbitrary strength....
1. Find the loss in stagnation pressure through a normal shock with an incoming flow at a Mach number of 2 and incoming...
1. Find the loss in stagnation pressure through a normal shock with an incoming flow at a Mach number of 2 and incoming flow stagnation pressure of 200 kPa(abs). In addition to the stagnation pressure downstream of the shock, also give the Mach number and (static) pressure downstream of the shock. DISCUSSION: Compare the "shock compression" (increase in STATIC pressure) obtained from the normal shock to the compression that would be obtained from an isentropic deceleration to the same Mach...
2. Find the Mach number and air speed corresponding of 500 kPa(abs) in an air flow with a (static) pressure of 100 kPa...
2. Find the Mach number and air speed corresponding of 500 kPa(abs) in an air flow with a (static) pressure of 100 kPa and measured (stagnation) temperature of 500 K. DISCUSSION: Suppose that, instead of assuming that a normal shock occurs upstream of the Pitot tube, it is assumed that the flow upstream is ISENTROPIC... what would the estimated flow speed be in that case? (NOTE: A normal shock is always observed to form upstream of bluff bodies such as...
Poblem Comergini sentropie regim (no shock waves) Consider isentropic flow through a converging-diverging nozzle. The exit...
Poblem Comergini sentropie regim (no shock waves) Consider isentropic flow through a converging-diverging nozzle. The exit area of the nozzle is , and the throat area of the nozzle is . The air entering the nozzle has stagnation conditions: , and Use Figure D.1 or Table D (a) Calculate the mass flow rate for choked flow (that is, sonic flow at the throat). Hints: See Section 11.7, use Figure D.1 to find density and temperature at M 1 (throat), find...
Both qualitatively and quantitatively understand how the properties of a flow change through a normal shock....
Both qualitatively and quantitatively understand how the properties of a flow change through a normal shock. Know why a normal shock is called a normal shock. Know what object shapes cause normal shocks to form, and what object shapes cause attached oblique shocks to form. Know where to find a normal shock or normal shocks on an airplane or rocket for any Mach number ldentify shocks in photographs, and characterize important parts of the flow (supersonic vs subsonic, etc) Qualitatively...
4. [25 pts] The pressure coefficient is defined as Cp = 1 Con = P —...
4. [25 pts] The pressure coefficient is defined as Cp = 1 Con = P — Poo POU Assuming incompressible flow, use the incompressible form of Bernoulli's equation to show that the value of Cp at a stagnation point is given by Cjosp = 1. Now assume isentropic compressible flow of a gas with constant specific heats and derive the following relation for the value of the pressure coefficient at a stagnation point: 2 sp /M% poo M. ! 2...
M 3. Consider a scenario in which supersonic flow is expanded and turned by 150 through...
M 3. Consider a scenario in which supersonic flow is expanded and turned by 150 through a Prandtl-Meyer expansion wave/fan. Consider the gas to be calorically perfect Air with upstream properties as follows: M1 = 4, P = 20 kPa, T = 250 K. Find: 0-150 M2 (a) freestream Prandtl-Meyer function, Vi. (b) downstream Mach number, M2. (c) downstream static pressure, P2. (d) downstream static temperature, T2.
Supersonic aircraft develop shock waves at the engine inlet when it flies supersonically. Consider the two...
Supersonic aircraft develop shock waves at the engine inlet when it flies supersonically. Consider the two types of engine inlets described as follows and calculate the total pressure recovery ratio for each engine inlet design when the aircraft flies at Mach 2.5. Take the specific heat ratio y to be 1.4. (a) A three-shock system (two oblique + one normal, external compression inlet) as shown in Fig. 1 Please note that the two blue arrows are not part of the...
4. Consider viscous laminar flow of water between two stationary parallel plates as shown with velocity...
4. Consider viscous laminar flow of water between two stationary parallel plates as shown with velocity given by u = elby - y2) where e, a, and b are constants and y = 0 at the bottom: eby - ey? F T (eby2-cys we LI a) (7 points) Find a in terms of e and b. b) (8 points) Find the shear stress at y = a. Is the shear stress ever zero? If so, where?
4. The inviscid potential flow solution for flow down against a horizontal flat plate is given...
4. The inviscid potential flow solution for flow down against a horizontal flat plate is given by Axy·If the speed and pressure at (xy)-(0,2) are given as Vo and Po , determine: (a) the value of A ; (b) the fluid speed ratio V/Vo and AP-(P- Po) at the points (0,0); (2,0) ; and (2,2) ; (c) The total downward force per unit width on the plate between (xy) (-2, 0) and (+2, 0)? ; (d) for a fluid particle...
Consider the steady, incompressible flow of depth h of a liquid of known density ρ and...
Consider the steady, incompressible flow of depth h of a liquid
of known density ρ and unknown viscosity µ down a flat plate as
shown in Figure 1. Air is the fluid above the liquid layer. The
force of gravity is in the vertical direction with acceleration g,
and the plate is at an angle θ with respect to the horizontal.
Assuming the coordinate system as shown, with x aligned with the
flow direction, and y normal to the plate,...
1. Find the loss in stagnation pressure through a normal shock with an incoming flow at a Mach number of 2 and incoming flow stagnation pressure of 200 kPa(abs). In addition to the stagnation pressure downstream of the shock, also give the Mach number and (static) pressure downstream of the shock. DISCUSSION: Compare the "shock compression" (increase in STATIC pressure) obtained from the normal shock to the compression that would be obtained from an isentropic deceleration to the same Mach...
2. Find the Mach number and air speed corresponding of 500 kPa(abs) in an air flow with a (static) pressure of 100 kPa and measured (stagnation) temperature of 500 K. DISCUSSION: Suppose that, instead of assuming that a normal shock occurs upstream of the Pitot tube, it is assumed that the flow upstream is ISENTROPIC... what would the estimated flow speed be in that case? (NOTE: A normal shock is always observed to form upstream of bluff bodies such as...
Poblem Comergini sentropie regim (no shock waves) Consider isentropic flow through a converging-diverging nozzle. The exit area of the nozzle is , and the throat area of the nozzle is . The air entering the nozzle has stagnation conditions: , and Use Figure D.1 or Table D (a) Calculate the mass flow rate for choked flow (that is, sonic flow at the throat). Hints: See Section 11.7, use Figure D.1 to find density and temperature at M 1 (throat), find...
Both qualitatively and quantitatively understand how the properties of a flow change through a normal shock. Know why a normal shock is called a normal shock. Know what object shapes cause normal shocks to form, and what object shapes cause attached oblique shocks to form. Know where to find a normal shock or normal shocks on an airplane or rocket for any Mach number ldentify shocks in photographs, and characterize important parts of the flow (supersonic vs subsonic, etc) Qualitatively...
4. [25 pts] The pressure coefficient is defined as Cp = 1 Con = P — Poo POU Assuming incompressible flow, use the incompressible form of Bernoulli's equation to show that the value of Cp at a stagnation point is given by Cjosp = 1. Now assume isentropic compressible flow of a gas with constant specific heats and derive the following relation for the value of the pressure coefficient at a stagnation point: 2 sp /M% poo M. ! 2...
M 3. Consider a scenario in which supersonic flow is expanded and turned by 150 through a Prandtl-Meyer expansion wave/fan. Consider the gas to be calorically perfect Air with upstream properties as follows: M1 = 4, P = 20 kPa, T = 250 K. Find: 0-150 M2 (a) freestream Prandtl-Meyer function, Vi. (b) downstream Mach number, M2. (c) downstream static pressure, P2. (d) downstream static temperature, T2.
Supersonic aircraft develop shock waves at the engine inlet when it flies supersonically. Consider the two types of engine inlets described as follows and calculate the total pressure recovery ratio for each engine inlet design when the aircraft flies at Mach 2.5. Take the specific heat ratio y to be 1.4. (a) A three-shock system (two oblique + one normal, external compression inlet) as shown in Fig. 1 Please note that the two blue arrows are not part of the...
4. Consider viscous laminar flow of water between two stationary parallel plates as shown with velocity given by u = elby - y2) where e, a, and b are constants and y = 0 at the bottom: eby - ey? F T (eby2-cys we LI a) (7 points) Find a in terms of e and b. b) (8 points) Find the shear stress at y = a. Is the shear stress ever zero? If so, where?
4. The inviscid potential flow solution for flow down against a horizontal flat plate is given by Axy·If the speed and pressure at (xy)-(0,2) are given as Vo and Po , determine: (a) the value of A ; (b) the fluid speed ratio V/Vo and AP-(P- Po) at the points (0,0); (2,0) ; and (2,2) ; (c) The total downward force per unit width on the plate between (xy) (-2, 0) and (+2, 0)? ; (d) for a fluid particle...
Consider the steady, incompressible flow of depth h of a liquid
of known density ρ and unknown viscosity µ down a flat plate as
shown in Figure 1. Air is the fluid above the liquid layer. The
force of gravity is in the vertical direction with acceleration g,
and the plate is at an angle θ with respect to the horizontal.
Assuming the coordinate system as shown, with x aligned with the
flow direction, and y normal to the plate,...
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