Question

A stream of water emerging from a faucet narrows as fails. The cross-sectional area of the soutis As -6.40 cm. water comes out of the spout at a speed of 33.2 cm/s, and the waterfalls h = 7.05 cm before iting the bottom of sink What is the cross-sectional area of the water stream just before it is the sink? a. 0.162 cm3 b. 1.74 cm3c. 6.21cm3d. 0.943cm3

Answer 1

The area of the water stream will be 1.74 cm^2

Step-by-step explanation:

initial velocity of water u = 33.2 cm/s

initial area = 6.4 cm^2

height of fall = 7.05 cm

final area before hitting the sink = ?

as the water falls down the height, it accelerates under gravity; causing the speed to increase, and the area to decrease.

first we find the velocity before hitting the sink

using

`v^(2) = u^(2) + 2gh` -----Newton's equation of motion

where v is the velocity of the water stream at the sink

u is the initial speed of the water at the spout

h is the height of fall

g is acceleration due to gravity, and it is positive downwards.

g = 981 cm/s^2

imputing relevant values, we have

`v^(2) = 33.2^(2) + (2 * 981 * 7.05)`

`v^(2) = 1102.24 + 13832.1 = 14934.34`

`v = √(14934.34)` = 122.206 cm/s

according to continuity equation,

A1v1 = A2v2

where A1 is the initial area

V1 = initial velocity

A2 = final area

V2 = final velocity

6.4 x 33.2 = 122.206 x A2

212.48 = 122.206 x A2

A2 = 212.48 ÷ 122.206 ≅ 1.74 cm^2