It is desired to infer the value of the loss coefficient of the valve–spigot combination in a household bathtub. As shown in Fig. P12.7, leading from the underground water main to the house is pipe of diameter D₁ and total length L₁, with one 90° bend. Inside the house are pipe segments of diameter D₂ and total length L₂. The interior pipe leading to the tub has seven 90° bends and an open gate valve. There is a total rise H from water main to tub spigot. The main and atmospheric pressures are P_m and P₀, respectively.

Water is supplied at a gauge pressure P_m − P₀ = 2.4 × 10⁵ Pa. All of the pipe is copper. The 3⁄4-inch exterior pipe has a length L₁ = 20 m and actual diameter D₁ = 1.9 cm. The 1⁄2-inch interior pipe has a length L₂ = 16 m and actual diameter D₂ = 1.4 cm. The rise is H = 4 m and the spigot diameter is approximately 2 cm. If the flow rate at 20 °C is 1.9 × 10^–4 m³/s when the tub valve is opened, what is the valve–spigot loss coefficient?

Transcribed Image Text:

Water Main Pm D₁ H Gate Valve D₂ Valve-Spigot Seven 90° Bends H 4₁ Figure P12.7 Part of a home plumbing system. وا Po Tub