Engineering
Physics
BernoulIis Equation and Equation of Continuity
Question

One end of a cylindrical pipe has a radius of 1.5 cm. Water (density = 1.0×103 kg/m3) streams steadily out at 7.0m/s. The rate at which mass is leaving the pipe is:

7.0kg/s

2.5kg/s

48 kg/s

4.9kg/s

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Solution
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The mass flow rate is given by the product of density (ρ), cross-sectional area (A), and velocity (v). The area of the circular pipe end is A = πr².

First, convert the radius to meters: r = 1.5 cm = 0.015 m.

Calculate the area: A=πr2=π×(0.015)27.0686×10-4m2

Now, calculate the mass flow rate:

dmdt=ρAv=(1000)×(7.0686×10-4)×(7.0)4.95kgs

This value is closest to 4.9 kg/s

Final Answer: 4.9kg/s