Fluid dynamics

[Busybee]

Water flows at the end of an aqueduct into the upper end of a 500m long pipe. The pipe has angle of 30 degrees to the horizontal and its low end exits into the bottom of a collection tank. The collection tank can hold a depth of 120m, above the centre line of the delivery pipe exit. Extra liquid can overflow the lip of the tank into a river.

The pipe tapers from a diameter of 2.0m at the top to 0.8m at the bottom. Assuming the head loss to be 8% of the potential head of the wateras it enters the pipe, determine the flow velocity of the water as it enters the collection tank.

I have worked out two CSA's for the pipe and are stuck. Should I use bernoulli's equation or the continuity equation to work out the flow velocity of the water?

 

[bjuveges]

Water flows at the end of an aqueduct into the upper end of a 500m long pipe. The pipe has angle of 30 degrees to the horizontal and its low end exits into the bottom of a collection tank. The collection tank can hold a depth of 120m, above the centre line of the delivery pipe exit. Extra liquid can overflow the lip of the tank into a river.

The pipe tapers from a diameter of 2.0m at the top to 0.8m at the bottom. Assuming the head loss to be 8% of the potential head of the wateras it enters the pipe, determine the flow velocity of the water as it enters the collection tank.

I have worked out two CSA's for the pipe and are stuck. Should I use bernoulli's equation or the continuity equation to work out the flow velocity of the water?

You should use the Bernoulli equation, the reason being is that continuity equation requires a steady velocity, since the head loss is at 8% when it enters the pipe, it cannot satisfy the continuity equation

Likewise, the Bernoulli equation necessarily only requires a steady flow, and that is the distinct factor separating the use between one or the other

So:Bernoulli's equation

Hope I helped

Brandon