Question

The figure below shows a stream of water in steady flow from a kitchen faucet. At the faucet, the diameter of the stream is 0.960 cm. The stream fills a 125-cm³ container in 16.0 s. Find the diameter of the stream 13.0 cm below the opening of the faucet.

Answer 1

Solution :

Here, Flow rate of water (Q) = 125 cm³ / 16 s = 7.8125 cm³/s


Volume flow rate = v₁ A₁
Q = v₁ (πd²/4)

v₁ = Q / (πd²/4)

v₁ = { 4(7.8125 cm³/s) } / {π(0.960 cm)²}

v₁ = 10.79 cm/s

The velocity of the water at the faucet : v₁ = 10.79 cm/s = 0.1079 m/s

Now, the velocity of the water 13.0 cm ( = 0.13 m) below the faucet is :
Using formula : (v₂)² = (v₁)² + 2ad

(v₂)² = (0.1079 m/s)² + 2(9.81 m/s²)(0.13 m)

(v₂)² = 2.56

v₂ = 1.6007 m/s = 160.07 cm/s

Now, Volume flow rate remains constant.

Thus : Volume flow rate = v₁ A₁ = v₂ A₂

Q = v₂ (πd²/4)

(d₂)² = 4 Q / (v₂ π) = 4(7.8125 cm³/s) / {(π)(160.07 cm/s)} = 0.062 cm²

Thus : d₂ = 0.249 cm