(a) Water flows through the nozzle of a garden hose. Find an expression for m˙ in terms of line pressure P₁, ambient pressure P₂, inside hose diameter D₁, and nozzle outlet diameter D₂. Assume steady flow, and isothermal, adiabatic operation. For liquid water modeled as an incompressible fluid, H₂ − H₁ = (P₂ − P₁)/ρ for constant temperature.
(b) In fact, the flow cannot be truly isothermal: we expect T₂ > T₁, owing to fluid friction. Hence, H₂ − H₁ = C (T₂ − T₁) + (P₂ − P₁)/ρ, where C is the specific heat of water. Directionally, how would inclusion of the temperature change affect the value of m˙ as found in Part (a)?