Question

In a horizontal pipe with a gradually decreasing cross-section (in the direction of flow) there is a clear fluid of unknown density. The pressure at point P is higher than the pressure at point Q by 260 Pa. A technician measures the fluid's velocity at point P as 0.37 m/s, and that at point Q as 0.77 m/s. What is the density of this clear fluid, in kg/m^3?

Answer 1

Answer:

the density of this clear fluid is 1140.35 kg/m^3

Explanation:

Given that :

$P_p = P__{Q}} + 260 \ Pa \\ \\ v_p =0.37 \ m/s \\ \\ v_Q = 0.77 \ m/s$

According to Bernoulli's Equation.

$P_p + \frac{1}{2} pv^2_p+pgh_p= P_Q+ \frac{1}{2} pv^2_Q + pgh_Q$

∴ $260 = \frac{1}{2}p (v^2_Q-v^2_p)$      since ( $h_p = h_Q$)

$\rho = \frac{2(260)}{v^2_Q-v^2_p}$

$\rho = \frac{2(260)}{0.77^2-0.37^2}$

$\rho = \frac{520}{0.5929-0.1369}$

$\rho =$ $1140.35 \ kg/m^3$