An airplane has two wings with an area of 75 m² each. Air flows over the top at 200 m/s and under the wings at 180 m/s. What is the net force on the wings due to the Bernoulli effect? (Take density of air 1.20 kg/m³)
An airplane has two wings with an area of 75 m² each. Air flows over the top at 200 m/s and under the wings at 180 m/s. What is the net force on the wings due to the Bernoulli effect? (Take density of air 1.20 kg/m³)
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![**Title: Calculating Net Force on Airplane Wings Using Bernoulli's Principle**
**Introduction:**
In this problem, we are given the specifications of an airplane's wings and are required to determine the net force on these wings due to the Bernoulli effect.
**Problem Statement:**
An airplane has two wings, each with an area of 75 m². Air flows over the top of the wings at 200 m/s and under the wings at 180 m/s. What is the net force on the wings due to the Bernoulli effect? (Assume the density of air is 1.20 kg/m³).
**Solution:**
To find the net force on the wings, we can use Bernoulli's equation which relates the pressure difference over the wings to the velocities of the airflows above and below the wings.
**Step-by-Step Calculation:**
1. **Calculate the pressure difference across the wings:**
Bernoulli's equation states that for an incompressible, frictionless fluid, the following relationship holds:
\[
P + \frac{1}{2} \rho v^2 = \text{constant}
\]
By considering the airflow above and below the wings:
\[
P_{\text{top}} + \frac{1}{2} \rho (v_{\text{top}})^2 = P_{\text{bottom}} + \frac{1}{2} \rho (v_{\text{bottom}})^2
\]
Rearrange to find the pressure difference (\( \Delta P \)):
\[
\Delta P = P_{\text{bottom}} - P_{\text{top}} = \frac{1}{2} \rho [(v_{\text{top}})^2 - (v_{\text{bottom}})^2]
\]
Substitute the given values (\( \rho = 1.20 \, \text{kg/m}^3 \), \( v_{\text{top}} = 200 \, \text{m/s} \), \( v_{\text{bottom}} = 180 \, \text{m/s} \)):
\[
\Delta P = \frac{1}{2} \times 1.20 \, \text{kg/m}^3 \times [(200 \, \text{m/s})^2 - (180 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38a5f9d6-9ba6-414e-a3d3-92c69a7c04d9%2F39f8c7f9-39e2-4f30-8e20-7ebfc1533d89%2Fauvbwy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Net Force on Airplane Wings Using Bernoulli's Principle**
**Introduction:**
In this problem, we are given the specifications of an airplane's wings and are required to determine the net force on these wings due to the Bernoulli effect.
**Problem Statement:**
An airplane has two wings, each with an area of 75 m². Air flows over the top of the wings at 200 m/s and under the wings at 180 m/s. What is the net force on the wings due to the Bernoulli effect? (Assume the density of air is 1.20 kg/m³).
**Solution:**
To find the net force on the wings, we can use Bernoulli's equation which relates the pressure difference over the wings to the velocities of the airflows above and below the wings.
**Step-by-Step Calculation:**
1. **Calculate the pressure difference across the wings:**
Bernoulli's equation states that for an incompressible, frictionless fluid, the following relationship holds:
\[
P + \frac{1}{2} \rho v^2 = \text{constant}
\]
By considering the airflow above and below the wings:
\[
P_{\text{top}} + \frac{1}{2} \rho (v_{\text{top}})^2 = P_{\text{bottom}} + \frac{1}{2} \rho (v_{\text{bottom}})^2
\]
Rearrange to find the pressure difference (\( \Delta P \)):
\[
\Delta P = P_{\text{bottom}} - P_{\text{top}} = \frac{1}{2} \rho [(v_{\text{top}})^2 - (v_{\text{bottom}})^2]
\]
Substitute the given values (\( \rho = 1.20 \, \text{kg/m}^3 \), \( v_{\text{top}} = 200 \, \text{m/s} \), \( v_{\text{bottom}} = 180 \, \text{m/s} \)):
\[
\Delta P = \frac{1}{2} \times 1.20 \, \text{kg/m}^3 \times [(200 \, \text{m/s})^2 - (180 \
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