Question

A bucket having area of cross sectional a has a small hole of area a at bottom is placed under a tap of water the rare of flow of water from tap is v m3/s the maximum height upto which water can be filled in bicket is

Answer 1

Answer:

v=√(2gh)

Explanation:

The basic formula for velocity of water flowing out of the small hole in the wall or in the bottom of the container can be derived from Bernoulli’s equation and is called Torricelli’s law:

Answer 2

Answer :

Maximum height upto which water can be filled in bucket is

h=v²/2g

Explanation :

Given :

Area of cross section of bucket = A

Let the density of liquid be ρ

A small hole is made at the bottom of the container at the depth h fom the free surface of container.

Let P be the atmospheric pressure.

Applying Bernoulli's equations at both points 1 and 2  [ top surface and bottom hole surface]

we get:

P+1/2 ρ(0)²+ ρgh=P+ ρg(0)+1/2  ρ v²

ρgh= 1/2  ρv²

v²=2gh

v=√2gh

this is the speed of a freely falling body at any point of height h during its fall.

The above equation is known as Torrecelli's law

so maximum height upto which water can be filled in bucket is

h=v²/2g