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Chapter 3: Problem 25

A Pitot-static tube is used to measure the velocity of helium in a pipe. The temperature and pressure are \(40^{\circ} \mathrm{F}\) and 25 psia. A water manometer connected to the Pitot-static tube indicates a reading of 2.3 in. Determine the helium velocity. Is it reasonable to consider the flow as ircompressible? Explain.

Short Answer

Expert verified
The velocity of helium can be calculated using the given conditions and the Pitot-static tube formula. Furthermore, the Mach number, calculated using the obtained velocity, would allow determining if the flow is incompressible. If the Mach number is close to or less than 0.3, the flow can be considered incompressible.

Step by step solution

01

Calculate velocity of helium

The velocity, v, of helium can be obtained using the Pitot tube formula: \(v = \sqrt{2g\Delta h}\), where g is the gravitational acceleration, and \(Delta h\) is the manometer reading. The \(Delta h\) is 2.3 inches, while g is approximately 32.2 ft/s². Convert \(Delta h\) to feet for the sake of uniformity: \(Delta h_{feet} = 2.3 / 12 \). Now you can substitute into the equation to obtain the velocity.
02

Calculate Mach Number

We can determine if the flow can be deemed as incompressible by calculating the Mach number, given by: \(Ma = v/c\), where c is the speed of sound in helium. If the Mach number is close to or less than 0.3 then the flow is generally considered as incompressible. c can be obtained by the formula \(c = \sqrt{v \cdot R \cdot T}\), where v is specific heat ratio (which is 1.66 for helium), R is the specific gas constant (2077 \( \frac{ft.lb_{f}}{lb_m.R} \)) and T is the absolute temperature in Rankine (40F converted to Rankine is \(40 + 460\)). Substitute these values in c formula first and then into Mach Number formula.
03

Evaluate the results

With the obtained Mach number, determine the nature of the flow. If the resulting Mach number is less than or equal to 0.3, the flow can be considered as incompressible. Conversely, if the Mach number is greater than 0.3, the flow isn't incompressible. This answers the second question.

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Most popular questions from this chapter

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