Question

Write a short paragraph to answer the question. The sketch shows an idealization of a garden hose of diameter D and length L connected to a pipe bib at a residence. Assume that the supply pressure ps upstream of the valve is constant. Assume that the faucet valve has no head loss because itis fully open. Thus, the only head loss is in the garden hose. a. Derive an equation for the mean velocity V of the water in terms of the friction factor and other relevant variables. b. How much will V change if L is doubled? Assume f remains constant. · Valve (fully open) Diameter (D) House

Answer 1

an Given! The sketch shown idealization of a garden hose of diometer & and length I connected to a pipe bib at residence. Assume that the supply pressure ps upstream of the value is constant. Assume valve losses is neglizible. This only the head loss in the gerden hose valvel fully open) bicmeter D. v 2 P wsters An equation of meen velocity y of the Apply Bernolii equation ble point and Ps Уа + Po sg + +3 کمال becase VVO ZF 22 + 22 the 28 h = Ps-Po also sg h = FLU² agg fLv² Ps-Po 29 D sg where, S2 (Ps-Pol D S v = average velocity f- friction factor of pipe © for atmospheric pressure. s-density of water. If V change if Lip doubled from eqh when, L'=22 then meen velocity, v 2 (Ps - Pox D I 2Lf v = 0.707 2 (Ps-Po D If new meen velocity ve 0.707 v 0.707 & first case meen velocity