Toricellis law ? proof ?

• webspherev6
In summary, the conversation discusses Toricelli's Law, which relates the height and volume of water in a reservoir to the acceleration due to gravity and the area of a hole at the bottom of the reservoir. The conversation then goes on to discuss a specific scenario where the reservoir is a cylinder with a circular hole at the bottom, and how to find the expression for y(t) in terms of V(t).

webspherev6

toricellis law ? proof ??

Homework Statement

Let y(t) and V(t) be the height (in m) and the volume of the water (m^3), respectively, in a resevoir at time t (in s). If the water leaks out through a hole of area a ( in m^2) at the bottom of the resevoir, Toricelli's Law states that dV/dt= -a(squareroot(2gy)) where g is the acceleration due to gravity.

Suppose that the resevoir is a cylinder of height 5m and radius 50cm and that the hole in the bottom is circular with radius 2.5cm. If we take g=10m/s^2, show that y satisfies dy/dt= -1/200(squareroot(5y))

The Attempt at a Solution

Well i figured the volume of the cylinder is (5/4)pi and area of small circle is 0.00196m^2 i don't know what to do next ?? please help ..

Express V(t) in terms of y(t).

What is Torricelli's law?

Torricelli's law, also known as Torricelli's theorem, states that the speed of fluid flowing out of an opening in a container is equal to the speed that an object would accelerate if it fell from the same height as the fluid's surface.

Who discovered Torricelli's law?

Italian physicist and mathematician Evangelista Torricelli discovered the law in the 17th century while studying the properties of air and water.

What is the proof for Torricelli's law?

The proof for Torricelli's law involves using Bernoulli's principle, which states that the total energy of a fluid remains constant as it flows. By equating the total energy of the fluid at the surface to the total energy at the opening, the equation for Torricelli's law can be derived.

Does Torricelli's law apply to all fluids?

Torricelli's law is a fundamental principle of fluid mechanics and applies to all types of fluids, including liquids and gases.

How is Torricelli's law used in real life?

Torricelli's law has many practical applications, such as determining the flow rate of a fluid through a pipe or nozzle, measuring the speed of a fluid in a wind tunnel, or calculating the thrust of a rocket engine.