Answer to Question #274734 in Astronomy | Astrophysics for Lisa

Question

A horizontal pipe is 2 cm in radius at one end and increases in size so that it is 5 cm in radius at

the other end. Water is pumped into the small end of the pipe at 10 m/s and a pressure of

300 kPa (kilopascal). Find the

a.) speed and

b.) pressure of the water at the pipe’s large end.

Answer 1

Explanations & Calculations

• Use the continuity equation to calculate the speed at the other end.

$\qquad\qquad \begin{aligned} \small A_1v_1&=\small A_2v_2 \end{aligned}$

• Calculate the are of the pipes at both ends in SI units: square meters.
• Then apply them to the above equation, the speed at the other end can then be found.

• Use Bernoulli's equation to calculate the pressure at the other end.

$\qquad\qquad \begin{aligned} \small P_1+\frac{1}{2}\rho v^2_1&=\small P_2+\frac{1}{2}\rho v_2^2 \end{aligned}$

• Here $\small \rho$ is the density of the fluid, water in this case.
• You know by now the speed at both ends. Substitute the known values accordingly and get the answer for the pressure at the other end.