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## Homework Statement

A stream of water flows downward from a tap. Assume that the water is in free fall once it leaves the tap, at which point its speed is v1, and the initial diameter of the water stream is A1.

(i) Find an expression for the speed v2 of the liquid as a function of the distance, h, it has fallen.

(ii) Combine this with the equation of continuity, to find an expression for the speed v2 in terms of the distance h and the cross-sectional areas at A1 and A2.

(iii) The cross-sectional area of the stream changes from 1.2 cm2 to 0.35 cm2 between the positions A1 and A2. Calculate the volume rate of flow of water from the tap, in cm3 s

## Homework Equations

Continuity equation

Kinematic equations

## The Attempt at a Solution

(i)

.5(v

_{1})

^{2}+ gh = .5(v

_{2})

^{2}

therefore v

_{2}= √(2*(.5(v

_{1})

^{2})+gh)

(ii)

.5(v

_{1})

^{2}+ gh = .5(v

_{2})

^{2}

therefore using A

_{1}v

_{1}= A

_{2}v

_{2}

.5(v

_{1})

^{2}+ gh = .5(v

_{1})

^{2}*A

_{1}/A

_{2}

and so

.5(v

_{1})

^{2}((A

_{1}/A

_{2})

^{2}- 1) = gh

therefore v

_{1}= √(2gh/(A

_{1}/A

_{2})

^{2}- 1)

(iii)

I'm not sure how you can get a numerical value for this question but the question seems to imply you can.

any help would be appreciated.