• Card 21 / 35: An incompressible fluid with density 0.55 kg/m3 flows through a contraction in a pipe from an ID of 0.5 in to an ID of 0.4 in at a flow rate of 0.0005 m3/s. Calculate the pressure change over the contraction according to Bernoulli's equation.
    A) 61.3 Pa
    B) 122 Pa
    C) 1116 Pa
    D) 6130 Pa
    E) 613 Pa

    Answer:
    E) 613 Pa

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Explanation:

First, one must recall Bernoulli's equation and how to use it. If necessary, you may want to review Bernoulli's equation in Unit 2 and practice memorizing this equation. For our purposes here, we will write it as v2/2 + P/r + gh = a constant. Because we are given no other information, we will assume that h (the elevation) is a constant over a streamline. The solution is then just a matter of calculating the velocities and then doing appropriate unit conversions. It is perhaps simplest to work in SI units. The two cross sections for flow are 1.27 x 10-4 m2 and 8.11 x 10-5 m2. Hence, the two velocities are 39.37 m/s and 61.5 m/s. Thus, the change in v2/2 = 1116 m2/s2. If we multiply this term by the density, we are left with units of Pascal for a pressure difference of 613 Pa.

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Thermal-Fluid Systems ME303

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Attribution:  Dr. Steve Gibbs. Thermal-Fluid Systems. The Saylor Academy 2014, http://www.saylor.org/courses/me303/
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