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 change if L is doubled? Assume f remains constant. Valve (fully open) Diameter (D) House

Answer 1

Assume steady flow → incompressible flow ✓ osv @ D 1 long the of Pipe 2 L diameter D density l Velocity of flow friction factor f (he) 3 eco P +V2 +Zi . so head loss is given by flv? adg Now apply Bernoulls equation P2 2² y Pg V = V2 Cuniform pipe) Zi=Zz Chorizontal pipe) P2 the + Zz the 25 so Pu flv? Po-P2 209 AP eg zdg 2 AP Pif 2 where AP:) Pressure difference D, if Pressure is in gauge Pressure then AP= Pi (gauge) or AP= P.-Patm =v Vz 2dAP

(T) .it then Lis Doubled velocity is v₂ V22 adap P 2(L) f Vzz z adap elf V, . 1 / V₂ = 0.7071 V