When a garden hose with an output diameter of 20 mm is directed straight upward, the stream of water rises to a height of 0.16 m . you then use your thumb to partially cover the output opening so that its diameter is reduced to 10 mm. how high does the water rise now?

the water rise is 2.56 m

Explanation:

Given data

diameter = 20 mm

height = 0.16 m

diameter is reduced = 10 mm

to find out

How high does the water rise

solution

we will apply here Bernoulis equation that is

Area  × velocity that is constant at starting point opening

so that A1V1 = A2V2        1  

and we know v = √(2gh)   2         from KE= PE,  ∵ 1/2mv² = mgh

and we know

area here = πd²/4

so from equation 1

A1V1 = A2V2

πd1²/4 × √(2gh1) = πd2²/4 × √(2gh2)

(d1/d2 )² √(2gh1)  =  √(2gh2)

so here d1 = 10 mm  and  d2 = 20 mm and h1 = 0.16 m put all value

400 / 100  √(2g0.16)  =  √(2gh2)

4√(2g0.16)  =  √(2gh2)

16× 2g × 0.16 = 2g × h2

h2 = 16 × 0.16

h2 = 2.56 m

so the water rise is 2.56 m