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laila [671]
1 year ago
15

Consider a propeller driven aircraft in forward flight at a speed of 150 mph: The propeller is set up with an advance ratio such

that the propeller disc average flow speed is 170 mph: The propeller diameter is 6 ft The aircratt flies at sea level: Calculate the thrust of the propeller: b. Calculate the induced velocity Calculate the velocity in the downstream far field away from the propeller disc Calculate the power absorbed by the fluid (energy added per unit mass mass flow rate) Calculate the propeller power (thrust flight speed) f. If propeller efficiency is defined by the ratio of e to d, calculate the propeller etficiency:
Mathematics
1 answer:
meriva1 year ago
8 0

a)  The thrust of the propeller is  23,834 lbf

b)  The induced velocity is 8.44 mph

c)  The velocity in the downstream far field away from the propeller disc     is 161.56 mph

d) The power absorbed by the fluid is  42.7 hp

e)  the propeller power (thrust flight speed) is  4,844.08 hp

f)  The propeller efficiency is 113.6%

a)The thrust of the propeller can be calculated using the equation,

Thrust = 2πρR^2V^2, where ρ is the air density, R is the propeller radius, and V is the average velocity of the propeller disc. For sea level at a speed of 150 mph, the air density is about 0.002377 slugs/ft^3.

the thrust of the propeller can be calculated as: Thrust = 2π x 0.002377 x (6 ft)^2 x (170 mph)^2 = 23,834 lbf

b)The induced velocity can be calculated using the equation v_ind = (1/2) V ∞ [1–(V_∞/V_tip)^2]^(1/2), where V_∞ is the free stream velocity and V_tip is the tip velocity of the propeller. For the given problem, the induced velocity can be calculated as: v_ind = (1/2) x 150 mph x [1–(150 mph/170 mph)^2]^(1/2) = 8.44 mph

c) The velocity in the downstream far field can be calculated using the equation V_∞ = V_tip – v_ind, where V_tip is the tip velocity of the propeller and v_ind is the induced velocity. For the given problem, the velocity in the downstream far field can be calculated as: V_∞ = 170 mph – 8.44 mph = 161.56 mph

d)The power absorbed by the fluid can be calculated using the equation P_fluid = (1/2) ρ V_ind^3 A_disc, where ρ is the air density, V_ind is the induced velocity, and A_disc is the area of the propeller disc. For the given problem, the power absorbed by the fluid can be calculated as P_fluid = (1/2) x 0.002377 x (8.44 mph)^3 x (π x (6 ft)^2) = 42.7 hp

e)The power absorbed by the propeller can be calculated using the equation P_prop = T x V, where T is the thrust of the propeller and V is the flight speed of the aircraft. For the given problem, the power absorbed by the propeller can be calculated as: P_prop = 23,834 lbf x 150 mph = 3,575,500 ft-lbf/s = 4,844.08 hp

f)The efficiency of the propeller can be calculated using the equation η = P_prop/P_fluid, where P_prop is the power absorbed by the propeller and P_fluid is the power absorbed by the fluid. For the given problem, the efficiency of the propeller can be calculated as: η = 4,844.08 hp/42.7 hp = 113.6%

To know  more  about induced velocity refer to the link brainly.com/question/15280442

#SPJ4

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