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

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

Step-by-step 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 + (1)/(2) pv^2_p+pgh_p= P_Q+ (1)/(2) pv^2_Q + pgh_Q`

∴
`260 = (1)/(2)p (v^2_Q-v^2_p)` since (
`h_p = h_Q`)

`\rho = (2(260))/(v^2_Q-v^2_p)`

`\rho = (2(260))/(0.77^2-0.37^2)`

`\rho = (520)/(0.5929-0.1369)`

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