Question

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?

Answer 1

Answer:

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