18 m (Another review problem) A helicopter of mass 10,000 kg hovers at sea level while carrying a load of 14,000 kg. The blades cause an 18-m-diameter air mass to move downward at an average velocity proportional to the overhead blade rotational velocity (i.e., V = ka, where k is 0.036 (m/s)/rpm). Determine 1. the wof the helicopter blades in rpm 2. the required power output Calculate this on a day where the atmospheric pressure is 102 kPa and the temperature is 25 °C. Assume air approaches the blades from the top through a large area with negligible velocity and air is forced by the blades to move down with a uniform velocity through an imaginary cylinder whose base is the blade span area. Load 14,000 kg

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
icon
Related questions
Question

This the problem how they give it to me I need help please quick

 

**Helicopter Aerodynamics and Power Calculation**

**Problem Statement:**

A helicopter with a mass of 10,000 kg hovers at sea level while carrying an additional load of 14,000 kg. The helicopter's blades cause an air mass with an 18-meter diameter to move downward at an average velocity that is proportional to the rotational velocity of the blades. The velocity is given by the equation \( V = k\omega \), where \( k = 0.036 \, \text{m/s/rpm} \).

Tasks:
1. Determine the angular velocity (\(\omega\)) of the helicopter blades in revolutions per minute (rpm).
2. Calculate the required power output for this operation.

Assumptions and Conditions:
- The day has an atmospheric pressure of 102 kPa and a temperature of 25°C.
- Air approaches the blades from the top with negligible initial velocity and moves downward with uniform velocity through an imaginary cylinder whose base matches the span area of the blades.

**Diagram Explanation:**

The diagram features:
- A helicopter shown in side view hovering with its rotor blades extending horizontally.
- A load of 14,000 kg hanging from the helicopter.
- The rotor blade span is indicated to be 18 meters.
- The helicopter and load form a simplified model to illustrate the forces and motion involved, with arrows representing the downward air movement caused by the rotor blades.
Transcribed Image Text:**Helicopter Aerodynamics and Power Calculation** **Problem Statement:** A helicopter with a mass of 10,000 kg hovers at sea level while carrying an additional load of 14,000 kg. The helicopter's blades cause an air mass with an 18-meter diameter to move downward at an average velocity that is proportional to the rotational velocity of the blades. The velocity is given by the equation \( V = k\omega \), where \( k = 0.036 \, \text{m/s/rpm} \). Tasks: 1. Determine the angular velocity (\(\omega\)) of the helicopter blades in revolutions per minute (rpm). 2. Calculate the required power output for this operation. Assumptions and Conditions: - The day has an atmospheric pressure of 102 kPa and a temperature of 25°C. - Air approaches the blades from the top with negligible initial velocity and moves downward with uniform velocity through an imaginary cylinder whose base matches the span area of the blades. **Diagram Explanation:** The diagram features: - A helicopter shown in side view hovering with its rotor blades extending horizontally. - A load of 14,000 kg hanging from the helicopter. - The rotor blade span is indicated to be 18 meters. - The helicopter and load form a simplified model to illustrate the forces and motion involved, with arrows representing the downward air movement caused by the rotor blades.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Knowledge Booster
Buckling of Columns
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY