Applications of Bernoulli’s principle

1. Statements based on Bernoulli’s principle are …

(1) lifting force on an aircraft

(2) hydraulic pump

(3) mosquito sprayers

(4) hot air balloon

Solution

Statements based on Bernoulli’s principle are

(1) lifting force on airplanes and

(3) mosquito sprayers

(2) Hydraulic pump under Pascal’s principle

(4) Air balloon based on Archimedes’ principle

2. Statements relating to the application of Bernoulli’s principle are …

(1) venturi meter

(2) mosquito sprayers

(3) barometer

(4) thermometer

Solution

Statements based on Bernoulli’s principle are

(1) venturi meter and

(2) mosquito spray

(3) a barometer based on hydrostatic pressure

(4) mercury thermometer or alcohol based on expansion

3. The tools based on Bernoulli’s principle are …

(1) hydraulic pump

(2) carburetor

(3) venturi meter

(4) thermometer

Solution

(2) carburetor and

(3) venturi meter

(1) hydraulic pump based on hydrostatic pressure, Pascal’s law

(4) mercury or alcohol thermometer based on expansion

4. Aircraft wings are designed to have maximum lift force, such as a picture. If v is the velocity of the air flow and P is the air pressure, then according to the Bernoulli principle, the design is made so that …

Solution

In order for the plane’s wings to lift upward, the air thrust at the bottom of the wing is larger than the thrust force on the top of the wing.

The thrust force on the underside of the wing is greater if the air pressure at the bottom of the wing is greater. P = F / A, where the pressure of P is directly proportional to F. If the pressure is greater then the force also increases.

Bernoulli’s principle states that the air pressure at the bottom of the wings is great when the air velocity at the bottom of the wing is small.

v_{A}> v_{B} so that P_{A} <P_{B}

**1. Question:** What is Bernoulli’s principle?

**Answer:** Bernoulli’s principle states that for an inviscid flow of a non-conducting fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid’s potential energy.

**2. Question:** How is Bernoulli’s principle related to the conservation of energy?

**Answer:** Bernoulli’s principle is a manifestation of the conservation of energy for fluid flows. The total energy in a steadily flowing fluid system is conserved. As the fluid’s kinetic energy (speed) increases, its potential energy (pressure) decreases, and vice versa.

**3. Question:** Why do airplane wings have a curved top and flat bottom?

**Answer:** Airplane wings (airfoils) are designed with a curved top and flat bottom to make air travel faster over the top than the bottom. According to Bernoulli’s principle, this causes lower pressure on the top and higher pressure on the bottom, leading to lift.

**4. Question:** How does Bernoulli’s principle explain the operation of a venturi meter?

**Answer:** A venturi meter has a constricted section where fluid speed increases, leading to a decrease in pressure. By measuring the pressure difference between the constricted and unconstricted sections, one can determine the fluid’s flow rate, utilizing Bernoulli’s principle.

**5. Question:** Why does a spinning soccer ball curve in its path?

**Answer:** This is due to the Magnus effect. As the ball spins, it speeds up air on one side and slows it down on the other. Based on Bernoulli’s principle, this leads to a pressure difference, causing the ball to curve.

**6. Question:** How does Bernoulli’s principle relate to the functioning of an atomizer or perfume sprayer?

**Answer:** When air is blown across the top of the atomizer tube, it speeds up, creating an area of low pressure. The higher pressure at the bottom pushes the liquid up the tube, where it meets the fast-moving air and is sprayed out in a fine mist.

**7. Question:** How does a curved roof on a building pose a risk during high winds?

**Answer:** During high winds, the air moves faster over a curved roof compared to a flat surface. Faster-moving air over the curved surface creates an area of low pressure, according to Bernoulli’s principle. This pressure difference can cause a lifting effect, potentially damaging the roof.

**8. Question:** Why do open windows in a moving car create a fluttering effect on papers inside?

**Answer:** As the car moves, the air speed outside is higher than inside the car. This creates a pressure difference due to Bernoulli’s principle, causing the papers to flutter as the air tries to equalize the pressure.

**9. Question:** How can Bernoulli’s principle explain the lift experienced by kite surfers?

**Answer:** The kite, when angled into the wind, speeds up the airflow over its top surface, creating an area of low pressure. The higher pressure underneath the kite, in comparison to the low pressure on top, creates a lift, allowing kite surfers to be lifted off the water.

**10. Question:** Why does a shower curtain get drawn inward when the water is turned on?

**Answer:** The hot water from the shower heats the air, making it rise and speeding up the airflow in the shower area. This faster-moving air creates a lower pressure inside the shower area compared to outside. As a result, the shower curtain is drawn inward due to the pressure difference explained by Bernoulli’s principle.