Problem Indicate whether the following statements are truc or-alse and provide b

Question

Problem Indicate whether the following statements are truc or-alse and provide brief justification to, your answers There will be no credit for unjustified answers and for justifications that are longer than three lines There can be incompressible ow in fluids the density of which varies (3 A sual room temperature, the spood.ot sound in osygen is higher than the speed of sound in hydrogen. (5%) At usual room temperature, the speest of sound in air at 10 bar is larger than the speed of sound in air at 1 bar, because at 10 bar the density is lager and the molecules are closer to cach other. (5%) d During the compressible flow of air across a nozzle, the temperature stays constant, e3%)

Explanation / Answer

a ) False

Incompressible fluid is a material property the density of the fluid is constant.

Incopressible flow describes a flow property:

In an incompressible flow the density of a fluid element does not change along its pathline (i.e. the material derivative of the density must vanish)

so you can have an incompressible flow of a compressible fluid (as alexis explains) in the case of low mach numbers or in stratified flows.

an incompressible fluid always results in an incompressible flow.

b) False

All for 20 oC, 1 Atm, audible frequencies. Speed of sound of Oxygen and Hydrogen

Oxygen=326 m/s

Hydrogen=1270m/s

Higher speed of the molecules means it can transmit pressure waves that much more quickly.Hydrogen molecules are only 1/8 the mass of oxygen molecules. So, at the same temperataure, hydrogen molecules must travel much faster in order to have the same kinetic energy, on average, per molecule.

c) Sound is merely molecules in air vibrating and colliding with each other thereby making sound travel. Assuming air pressure as 1atm normal and doubling it to become 2atm would only bring molecules closer to each other thereby hampering negligibly the way air molecules vibrate. Since temperature change is the phenomena responsible for greater molecular collisions, the soles of sound is relatively independent of pressure but varies largely with temperature.

d) True

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