An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 30.0 degrees. The narrow section is 15.0 m from the wide section and the narrow section is lower than the wide section. The velocity of the fluid in the wide section of the pipe is 4.00 m/s and the velocity of the fluid in the narrow section of pipe is 9.00 m/s. The pressure of the fluid in the wide section is 250 kPa. What is the pressure in the narrow section of the pipe? (density of the fluid is 1,000 kg/m³) A) 260 kPa B) 275 kPa C) 291 kPa D) 301 kPa E) 320 kPa

Question

Quizplus · Accepted Answer

We can use Bernoulli's equation to solve this problem. Bernoulli's equation states that:

$P_1 + \frac{1}{2}ho v_1^2 + ho g h_1 = P_2 + \frac{1}{2}ho v_2^2 + ho g h_2$

Where $P$ is the pressure, $ho$ is the density, $v$ is the velocity, $g$ is the acceleration due to gravity, and $h$ is the height above some reference point.

We can use this equation to solve for the pressure in the narrow section of the pipe:

$P_2 = P_1 + \frac{1}{2}ho(v_1^2 - v_2^2) + ho g (h_1 - h_2)$

We are given that $P_1 = 250$ kPa, $ho = 1000$ kg/m$^3$, $v_1 = 4$ m/s, $v_2 = 9$ m/s, $h_1 = 0$, and $h_2 = -15$ sin(30.0) = -7.5 m.

Plugging in these values, we get:

$P_2 = 250 	ext{ kPa} + \frac{1}{2}(1000 	ext{ kg/m}^3)(4 	ext{ m/s})^2 - \frac{1}{2}(1000 	ext{ kg/m}^3)(9 	ext{ m/s})^2 + (1000 	ext{ kg/m}^3)(9.81 	ext{ m/s}^2)(-7.5 	ext{ m})$

$P_2 = 291$ kPa

Therefore, the answer is C) 291 kPa.

An Incompressible Fluid Is Flowing Through a Pipe with a Constriction