A hovercraft weighs M = 1500 kg and hovers without changing altitude. The exit flow exhausts to atmospheric pressure at sea-level. The flow is steady, incompressible and uniform properties can be assumed on all control surfaces. Assume air density = 1.22 kg/m'. In your solution, write all equations using variables names. Only plug in numerical values in part d). Hint: Use gage pressures. a) Apply and simplify the integral momentum equation in the vertical direction. Write your resulting equation here. Hints: The static pressure of the inlet flow is not at atmospheric pressure. Since the hovercraft is hovering without changing altitude, the net vertical force on the hovercraft from the airflows, pressure forces, and hovercraft weight must equal zero. b) Apply the Bernoulli equation between the inlet and a point 0 above the hovercraft where the air velocity is zero and the static pressure is atmospheric pressure. Ignore elevation changes between point 0 and the inlet. A simple equation for Pinlet, g (the gage pressure at the inlet) will result, write it here. c) Combine your equations from parts a) and b) with a simple mass conservation equation (between the inlet and exit) to find an equation for the exit velocity Vexit =f (M, g, p, Ainlet, Aexit).
A hovercraft weighs M = 1500 kg and hovers without changing altitude. The exit flow exhausts to atmospheric pressure at sea-level. The flow is steady, incompressible and uniform properties can be assumed on all control surfaces. Assume air density = 1.22 kg/m'. In your solution, write all equations using variables names. Only plug in numerical values in part d). Hint: Use gage pressures. a) Apply and simplify the integral momentum equation in the vertical direction. Write your resulting equation here. Hints: The static pressure of the inlet flow is not at atmospheric pressure. Since the hovercraft is hovering without changing altitude, the net vertical force on the hovercraft from the airflows, pressure forces, and hovercraft weight must equal zero. b) Apply the Bernoulli equation between the inlet and a point 0 above the hovercraft where the air velocity is zero and the static pressure is atmospheric pressure. Ignore elevation changes between point 0 and the inlet. A simple equation for Pinlet, g (the gage pressure at the inlet) will result, write it here. c) Combine your equations from parts a) and b) with a simple mass conservation equation (between the inlet and exit) to find an equation for the exit velocity Vexit =f (M, g, p, Ainlet, Aexit).
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:A hovercraft weighs M = 1500 kg and hovers without changing altitude. The exit flow
exhausts to atmospheric pressure at sea-level. The flow is steady, incompressible and
uniform properties can be assumed on all control surfaces. Assume air density = 1.22
kg/m'.
In your solution, write all equations using variables names. Only plug in numerical values
in part d).
Hint: Use gage pressures.
a) Apply and simplify the integral momentum equation in the vertical direction. Write
your resulting equation here. Hints: The static pressure of the inlet flow is not at
atmospheric pressure. Since the hovercraft is hovering without changing altitude, the
net vertical force on the hovercraft from the airflows, pressure forces, and hovercraft
weight must equal zero.
b) Apply the Bernoulli equation between the inlet and a point 0 above the hovercraft
where the air velocity is zero and the static pressure is atmospheric pressure. Ignore
elevation changes between point 0 and the inlet.
A simple equation for Pinlet, g (the gage pressure at the inlet) will result, write it here.
c) Combine your equations from parts a) and b) with a simple mass conservation
equation (between the inlet and exit) to find an equation for the exit velocity
Vexit =f (M, g, p, Ainlet, Aexit).
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