Torricelli's Theorem

height of water (m)

5

radius of tank (m)

4

height of spigot (m)

0.5

radius of spigot (m)

0.25

velocity of efflux = 9.4870 m/s

range = 3.0000 m

Torricelli's theorem states that the velocity of efflux for a nonviscous fluid flowing from a cylindrical tank is

v=

2gh

where

g

is the acceleration due to gravity (10

m/

2

s

) and

h

is the distance between the surface of the water and the location of the spigot. However, this does not specify the exact coefficient because it assumes that the velocity of the water at the surface of the tank is negligible and that both the tank and the spigot are exposed to atmospheric pressure. If the velocity of the water at the surface is taken into account, the formula for the velocity of efflux becomes

v=

(2gh)1-

4

r

R

, where it takes into account

r

, the radius of the spigot, and

R

, the radius of the cylindrical tank. This equation can be derived from Bernoulli's equation,

p

1

+ρg

y

1

+

1

2

ρ

2

v

1

=

p

2

+ρg

y

2

+

1

2

ρ

2

v

2

, and the continuity equation,

A

1

v

1

=

A

2

v

2

.