1. Water pumping To supply the city of Oz, water must be pumped from a once-mighty river to the top of a small mountain.

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1 Water Pumping To Supply The City Of Oz Water Must Be Pumped From A Once Mighty River To The Top Of A Small Mountain 1 (99.02 KiB) Viewed 18 times

1. Water pumping To supply the city of Oz, water must be pumped from a once-mighty river to the top of a small mountain. This problem asks you to calculate the required head and power required for pumping. It is conventional in water hydraulics to express the needed pressure in terms of the total head of water, which is due to the elevation change (h), plus the head loss (hloss due to the friction of moving water in a pipe. The head is equivalent to the pressure created by the height of a column of water due to gravity Ap = pgh, where p is the mass density of water, g is the gravitational constant and h is the height of the column. If water moves with velocity V through a pipe of diameter D and of length L, the head loss LV2 hross = ff where fis a dimensionless "friction factor” that accounts for the viscosity of the water Dg and non-laminar flow within the pipe. Quantities needed in the problem (rounded off for simplicity): The elevation changes from 100 m at the river to 1.1 km in Oz The pipe L = 10 km with an internal diameter D = 20 cm The flow velocity V = 1 m/s The friction factor f = 0.01 The density of water p = 109 kg/m2 The gravitational constant g = 9.8 m/s2 The efficiency for the pump (electric motor plus impeller) = 50 %. a. What is the flow rate of water in m/hour? b. How much head [m] is associated with raising the water elevation from the river to the mountain? C. How much head loss [m] is associated with water flow through the pipe (i.e., not considering the change in elevation)? d. What is the power input [kW] required to deliver water to Oz? Note: The above delivers water to Oz with zero pressure at the point of delivery (the green door of the castle, if you know the movie). In an actual water distribution system, we would add additional pressure in order to flow water through the distribution system. Do not consider that need here.