A level pipe contains a nonviscous,incompressible fluid with a density 1200 kg/m³ that is flowing steadily.At one position within the pipe,the pressure is 300 kPa and the speed of the flow is 20.0 m/s.At another position,the pressure is 200 kPa.What is the speed of the flow at this second position? A)567 m/s B)16.2 m/s C)32.9 m/s D)23.8 m/s E)186 m/s

Question

Quizplus · Accepted Answer

Using Bernoulli's equation, we can write:
$$P_1 + \frac{1}{2}ho v_1^2 = P_2 + \frac{1}{2}ho v_2^2$$
where $P_1$ and $v_1$ are the pressure and speed at the first position, $P_2$ and $v_2$ are the pressure and speed at the second position, and $ho$ is the density of the fluid.

Plugging in the given values, we get:
$$300	ext{ kPa} + \frac{1}{2}	imes 1200	ext{ kg/m}^3	imes (20.0	ext{ m/s})^2 = 200	ext{ kPa} + \frac{1}{2}	imes 1200	ext{ kg/m}^3	imes v_2^2$$
Simplifying and solving for $v_2$, we get:
$$v_2 = \sqrt{\frac{(300 - 200)	ext{ kPa}}{0.5	imes 1200	ext{ kg/m}^3}} = 23.8	ext{ m/s}$$
Therefore, the answer is D.

A Level Pipe Contains a Nonviscous,incompressible Fluid with a Density