Question

If each of the seven individuals pulls water in with a velocity of 3.0 mm per second through an incurrent siphon 1.0 mm in diameter, and the combined water from all seven individuals exits the shared excurrent siphon, which has a diameter of 1.5 mm, what is the velocity of the water as it leaves the excurrent siphon?

Answer 1

We have,

Diameter of an incurrent siphon

Radius of an incurrent siphon

Diameter of excurrent siphon

Radius of excurrent siphon

Cross-sectional area of an incurrent siphon

Cross-sectional area of excurrent siphon

velocity of water through an incurrent siphon

let, velocity of water through an excurrent siphon =  

Volume flow-rate in incurrent siphon ( rate at which a volume of water passes through a cross-section of incurrent siphon ) is given as,

Cross-sectional area of an incurrent siphon   velocity of water through incurrent siphon

net volume flow-rate of incoming water   = number of incurrent siphons   volume flow-rate in single incurrent siphon

_________________________________________relation 1

Similarly,

Volume flow-rate in excurrent siphon ( rate at which volume of water passes through a cross-section of excurrent siphon ) is given as,

Cross-sectional area of an excurrent siphon   velocity of water through excurrent siphon

__________________________________________relation 2

Since water is incompressible,

The net rate at which water enters the seven incurrent siphons is equal to the rate at which water leaves the excurrent siphon.

that is,

Volume flow-rate of water in excurrent siphon =  net volume flow-rate of incoming water

using relation 1 and 2 in above equality we get,

Using above given values of in above equation we get,