Show that for the flow of a viscous fluid through a pipe, as analyzed in Box 29 1, the energy per unit mass dissipated as thermal energy by viscous forces is dQ dm p , where p is the pressure difference between the ends of the pipe The answer is independent of the viscosity and the cross sectional ...

Use conservation of energy in a fashion similar to the derivation o ...

Show that for the flow of a viscous fluid through a pipe, as analyzed in Box 29.1,

Question:

Show that for the flow of a viscous fluid through a pipe, as analyzed in Box 29.1, the energy per unit mass dissipated as thermal energy by viscous forces is dQ/dm = Δp/ρ, where Δp is the pressure difference between the ends of the pipe. The answer is independent of the viscosity and the cross-sectional shape of the pipe. Suppose water is forced through a pipe by a pressure difference of 10 atm. How much does it heat up?

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