The citizens of Rome were charged for water based on the size of the water pipe
ID: 1710303 • Letter: T
Question
The citizens of Rome were charged for water based on the size of the water pipe entering their house. Madame Fluid Mechanides, who learned about fluid dynamics from her real-life experience, attached a hose to the pipe as shown below. The pipe and hose have the same diameter. Given the data provided below, determine: (a) The volumetric flow rate before and after the change. (b) Velocity components (both horizontal and vertical) at location 2, assuming that the exit velocity at the pipe is horizontal. (c) Stagnation pressure at locations 1 and 2. Does your answer make sense? (d) Her husband, Mr. Soild Mechanides, wished to have a larger flow rate so that he could fill up his bathtub faster. What could Madame Fluid Mechanides do? She knew that"go jump into a lake" could not be an answer, knowing her husband's hot temperament. Note that replacing the existing pipe with a larger diameter pipe is not an option since it will increase the water bill.Explanation / Answer
(a) When the hose pipe is connected the available head got increased by 1m, which increased the velocity. With the same diameter, but increased velocity, the discharge or flow rate gets increased.
(b) assuming the hose takes the shape of the free flow of water, and there are no losses, horizontal component of the water remains the same as in pipe. Vh = Sq. root(2*g*h) = Sq. root(2*9.81*9) = 13.288 m/sec
while the vertical component can be found using Vy2-Uy2 = 2.g.s => Vy2 = 2*9.81*1 => Vy = 4.429 m/sec
(c) Stagnation pressure is the pressure when the velocity is zero. So just assume that the total head is converted into the pressure head.
Stagnation Pressure = unit weigt of water * available head = 9.81*10 = 98.1 kN/m2 (same for 1 and 2, as they have same water head of 10m)
It makes sense if the hose end are closed at both points, so that velocity is zero.
(d) (1) One can use a uniformly varying diameter hose, so that it has a diameter equal to that of pipe at the junction with pipe, while a large diameter at the outlet end. It must designed for minimum energy losses, just like venturimeter is designed.
(2)The hose must be frictionless, means very smooth, so that the friction losses are minimum.
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