A bicycle tire is fi lled with air at an absolute pressure of169.12 kPa, and the temperature inside is 30.0 °C. Supposethe valve breaks, and the air starts to exhaust out of the tireinto the atmosphere (pa = 100 kPa absolute and Ta =20.0 °C). The valve exit is 2.00 mm in diameter and is thesmallest cross-sectional area of the entire system. Frictionallosses can be ignored here; one-dimensional isentropicflow is a reasonable assumption. (a) Find the Machnumber, velocity, and temperature at the exit plane of thevalve (initially). (b) Find the initial mass flow rate out ofthe tire. (c) Estimate the velocity at the exit plane using theincompressible Bernoulli equation. How well does thisestimate agree with the “exact” answer of part (a)? Explain.
A bicycle tire is fi lled with air at an absolute pressure of
169.12 kPa, and the temperature inside is 30.0 °C. Suppose
the valve breaks, and the air starts to exhaust out of the tire
into the atmosphere (pa = 100 kPa absolute and Ta =
20.0 °C). The valve exit is 2.00 mm in diameter and is the
smallest cross-sectional area of the entire system. Frictional
losses can be ignored here; one-dimensional isentropic
flow is a reasonable assumption. (a) Find the Mach
number, velocity, and temperature at the exit plane of the
valve (initially). (b) Find the initial mass flow rate out of
the tire. (c) Estimate the velocity at the exit plane using the
incompressible Bernoulli equation. How well does this
estimate agree with the “exact” answer of part (a)? Explain.
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