A cylindrical bucket, open at the top, is 28.0 cm high and 11.0 cm in diameter. A circular hole with a cross-sectional area 1.55 cm2 is cut in the center of the bottom of the bucket. Water flows into the bucket from a tube above it at the rate of 2.46*10-4 m3/s. Part A How high will the water in the bucket rise

so height is 0.1283 m

Explanation:

given data

height = 28 cm

diameter = 11 cm

cross-sectional area = 1.55 cm2

water flow rate = 2.46*10^-4 m3/s

to find out

How high will the water in the bucket rise

solution

we know that here

potential energy = kinetic energy

mgh = 1/2 mv²

multiply both sides by the 2 and we get

2mgh=mv²

solve it we get

√ (2gh) = v ... 1

h = v²/2g ... 2

and

flow rate = A V

2.46*10^-4 = V 1.55*10^-4

V = 1.5870 m/s

so from 2

h = v²/2g

h = 1.5870² / 2 (9.81)

h = 0.1283 m

so height is 0.1283 m