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A stream of water from a kitchen faucet narrows as it fall. At the faucet, the diameter of the stream is 0.840 cm. The stream fills a 115-cm3 container in 15.6 s. a) What is the speed of the water just as it comes out of the faucet ? [4] b) What is the pressure in the water stream as the water comes out of the faucet ? [2] c) Write down the Bernoulli’s equation for the stream and find the speed of the water 24.0 cm below opening of the faucet.

Respuesta :

Answer:

Explanation:

In terms of volume of water per unit time , the speed of water flow =

115 / 15.6 cm³ / s

= 7.37 cm³ / s

radius of faucet = .42 cm

cress sectional area

A = π x .42²

= .5539 cm²

a )

If speed of flow at the time of coming out be v

v x A = volume rate of flow

v x .5539 = 7.37

v = 13.3 cm /s

b )

pressure = atmospheric pressure will work at that point .

c )

Applying Bernoulli's theorem for points at the opening of faucet and a point 24 cm below .

P + 1/2 ρv² + ρ gh = constant

P + 1/2 ρv₁² + ρ gh₁ = P + 1/2 ρv₂² + ρ gh₂

1/2 ρ (v₂² - v₁² ) = ρ g(h₁-h₂ )

.5 x 1 ( v₂² - 13.3² ) = 1 x 981 x  24

v₂² - 13.3² =  47088

v₂² = 47264.89

v₂ = 217.4 cm /s

= 2.17 m /s