Answer to Question #274723 in Astronomy | Astrophysics for Lisa

Question

A very wealthy woman who loves soda builds her house with a cylindrical pipe that transports Mountain Dew from downstairs to her upstairs bedroom. The Mountain Dew enters the house downstairs via a pipe with a cross sectional area of 0.0036 m2 where it is traveling with a speed of 0.48 m/ s . At the wealthy lady's bedroom, the faucet pipe through which the Mountain Dew exits has an area of 0.0012 m2. What is the speed of the Mountain Dew as it exits the faucet pipe in the lady's bedroom?

Answer 1

Explanations & calculations

• Mountain Dew behaves as an incompressible fluid hence the volumetric flow at any part of the pipe is the same.
• Therefore, considering the volumetric flow at the entrance and the outlet you can calculate the speed at the output.

$\qquad\qquad \begin{aligned} \small A_1v_1&=\small A_2v_2\\ \small v_2&=\small \frac{0.0036\,m^2\times0.48\,ms^{-1}}{0.0012\,m^2}\\ &=\small 1.44\,ms^{-1} \end{aligned}$

• The faucet reduces the area thereby increasing the speed.