Question

A Pitot-static tube is mounted on a 2.5 cm pipe where oil (???? = 860 kg/m3, ???? = 0.0103 kg/m·s) is flowing. The Pitot tube is positioned such that the local velocity measured is similar to the mean velocity through the pipe cross section. The pressure difference is measured to be 95.8 Pa. Find the volumetric flow rate in m3/s.

Answer 1

To find the volumetric flow rate in m3/s, we can use the equation Q = ρAv, where Q is the volumetric flow rate, ρ is the density of the oil, A is the cross-sectional area of the pipe, and v is the mean velocity through the pipe. Using the given pressure difference and the fact that the Pitot tube measures the local velocity similar to the mean velocity, we can solve for the volumetric flow rate.

Step-by-step explanation:

To find the volumetric flow rate in m3/s, we can use the equation:

Q = ρAv

Where Q is the volumetric flow rate, ρ is the density of the oil, A is the cross-sectional area of the pipe, and v is the mean velocity through the pipe. We are given the pressure difference, which is related to the mean velocity through Bernoulli's equation:

p = ½ρv2

Using these equations along with the given values and the fact that the Pitot tube measures the local velocity similar to the mean velocity, we can solve for the volumetric flow rate:

95.8 = ½(860)(0.0103)v2

v = √(2(95.8)/(860)(0.0103))

Once we have the mean velocity, we can calculate the cross-sectional area using the formula A = πr2, where r is the radius. With the known radius of 2.5 cm, we can find the area and then calculate the volumetric flow rate:

A = π(0.025)2

Q = (860)(0.0202)(√(2(95.8)/(860)(0.0103)))

Q ≈ 0.051 m3/s