# Fluids in motion (Bernoulli's equation)

• Lunar Guy
In summary, the conversation discusses the time required to fill a bucket with water from a garden hose. It is mentioned that covering the nozzle with a thumb will double the speed of the water, but it is unsure if this will affect the time it takes to fill the bucket. No equations are required to solve this problem.
Lunar Guy
1. The time required to fill a bucket with water from a certain garden hose is 30.0 s. If you cover part of the hose's nozzle with your thumb so that the speed of the water leaving the nozzle doubles, how long does it take to fill the bucket?

2. Homework Equations : None required. I hope. Just in case: A1v1 = A2v2

3. I believe that it would take the same amount of time to fill the bucket with water with your thumb on the nozzle than it would without your thumb on the nozzle... But I'm not sure...

Bump. Can anyone help me out?

Your intuition is correct! According to Bernoulli's equation, as the speed of a fluid increases, its pressure decreases. In this case, by covering part of the nozzle with your thumb, you are increasing the speed of the water. However, this also means that the pressure inside the hose decreases, which results in a decrease in the rate at which water flows out. Therefore, the time it takes to fill the bucket would remain the same. This is because the volume of water flowing out of the hose per second (flow rate) is the same in both cases, so the total volume of water in the bucket would also be the same.

## 1. What is Bernoulli's equation?

Bernoulli's equation is a fundamental principle in fluid mechanics that relates the pressure, velocity, and elevation of a fluid in motion. It states that as the speed of a fluid increases, the pressure decreases, and vice versa.

## 2. How is Bernoulli's equation derived?

Bernoulli's equation is derived from the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred. In fluid mechanics, this means that the total energy of a fluid remains constant as it moves through a system. Bernoulli's equation is a mathematical representation of this principle.

## 3. What are some applications of Bernoulli's equation?

Bernoulli's equation has many practical applications in engineering and science, including calculating the lift of an airplane wing, the flow of water through pipes, and the operation of carburetors in cars.

## 4. How does Bernoulli's equation relate to the Bernoulli effect?

The Bernoulli effect is a phenomenon that occurs when a fluid flows through a constricted area, such as a pipe or nozzle. According to Bernoulli's equation, as the fluid's velocity increases, its pressure decreases. This creates a pressure difference that can cause objects, such as ping pong balls, to move towards the faster-moving fluid.

## 5. What are the limitations of Bernoulli's equation?

Bernoulli's equation is based on several assumptions, including the fluid being inviscid (having no internal friction) and incompressible. In real-world situations, these assumptions may not hold true, so Bernoulli's equation may not accurately predict fluid behavior. Additionally, it only applies to steady, incompressible flows, so it cannot be used for turbulent or compressible flows.

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