Algebra1

COxford:

Water collected in a rain barrel can be used to water plants and reduce city water use. Water flowing from an open rain barrel has a velocity v=8h1/2, where v is in feet per second and h is the height of the water in feet. Find the height of the water if it is flowing at 16 feet per second.

Square both sides of the equation; rearrange to get h on its own; plug in the given value of v and calculate h, (I'm assuming that the units of the 'number' 8 are such that the result will be so many feet!).

Alan wrote:
COxford wrote:Water collected in a rain barrel can be used to water plants and reduce city water use. Water flowing from an open rain barrel has a velocity v=8h1/2, where v is in feet per second and h is the height of the water in feet. Find the height of the water if it is flowing at 16 feet per second.


Square both sides of the equation; rearrange to get h on its own; plug in the given value of v and calculate h, (I'm assuming that the units of the 'number' 8 are such that the result will be so many feet!).


Thanks Alan,
What did you interpret 8h1/2 to actually mean?

Melody:

Alan wrote:
COxford wrote:Water collected in a rain barrel can be used to water plants and reduce city water use. Water flowing from an open rain barrel has a velocity v=8h1/2, where v is in feet per second and h is the height of the water in feet. Find the height of the water if it is flowing at 16 feet per second.


Square both sides of the equation; rearrange to get h on its own; plug in the given value of v and calculate h, (I'm assuming that the units of the 'number' 8 are such that the result will be so many feet!).


Thanks Alan,
What did you interpret 8h1/2 to actually mean?

OrificeEqn.PNG

That is impressive.
Thanks Alan

This is a unit form of Torricelli's Law, it is derivable from Bernoulli's equations.
The correct form of the equation is velocity v = 8 Sqrt(h) or v =8 *h ^(1/2).

Torricelli's Law: v= sqrt (2gh(t)): v = velocity; g= acceleration of gravity; h(t)= is height of water at any given time. The time component is used because the flow rate will change (diminish) as the water drains. Here, only the initial conditions are under consideration, so the time (t) component of (h(t)) is 1.
With feet as the unit in the unit form
g=32 feet/s^2 (aprox), set initial unit h=1: sqrt(2*32*1) = 8

That is impressive too.
Thank you DavidQD

Looks like I have got some home work to try and work it all out. I think I will need to be considerable more awake for that task.

That is not shock - that is me trying to keep my eyes open.