Question

3. Water is pumped at an initial pressur floor of an apartment building. The pipe is 8.5 in a at an initial pressure of 60.0 psi in the basement to a vertical height of 21.0 m on the eighth apartment building. The pine is 8.5 inches in diameter in the basement, but in the eighth floor apartments, the pipes are only 0.75 inches in diameter. a) What is the pressure of the water in the pipes on the eighth floor if all the spigots are closcar b) What is the velocity of the water in the basement pipe and what is the velocity in an eighth floor pipe if one spigot is open? ) What is the velocity of the water in the basement pipe if 10 eighth floor spigots are open and water is flowing from all?

Answer 1

a)

The water inside the pipe has a varying pressure according to the depth of the level which is zero at the top and maximum at the bottom according to the equation P = hdg,

where h is the depth, d is the density and g is acceleration due to gravity.

but according to pascals law, if a pressure is applied in a continuous fluid in equilibrium, the pressure is equally distributed to all parts of the liquid. so the pressure applied by the pump at the bottom will be same at the eighth floor.

The pressure at the pipes at 8th floor = 60 psi

b)Let $v_{1}$ be the velocity of water at the bottom and $v_{2}$ be the velocity at eighth floor. And all the suffixes 1 represent the bottom level and suffixes 2 represent the eighth floor.

Accudng ualion ntnuitay 0072--0 A cndiny do Benoul's thuwrum, -R Ph 413685 000xCy-v)+ 1000x9-9 A2I 41368s Pa Saluaing and 2-(0 0078 V2 - 41S.77 yo.9994 - 415.7 4 IS. 9 40m/s CAn) 2

c)

Simi l A Vi= o x AoV2 Vi = o.07 Va -0 also 2 4 Is7 - .08 2 2 x o.9939 = GIS.7 Chmo) = 20.45 /s. - 0.078 2 . ZO 048 xdo 4s 2