Question

Elevated water tanks are used in a municipal water distribution system to provide adequate pressure. Compute the height (h) of the water tank above the ground surface to provide a static pressure of 410 kPA (60 psi). Compute the pressure in a building that is 12 m (40ft) above the ground surface. Typically, the pressure in a water distribution will range from (275 to 620 kPa) (40-90 psi). Compute the range in h corresponding this range in pressure. If the range in pressure is greater than this, multiple pressure zones may be required for the water distribution system. Are multiple pressure zones needed

Answer 1

a) h = 53.8 m, b) h_minimum = 28 m, h_maximum = 63.3 m

Step-by-step explanation:

a) For this exercise let's use Bernoulli's equation.

The subscript 1 is for the tank and the subscript for the building

P₁ + ½ ρ g v₁² + ρ g y₁ = P₂ + ½ ρ g v₂² + ρ g y₂

In general, the water tanks are open to the atmosphere, so P1 = Patm, also the tanks are very large so the speed of the water surface is very small v₁=0 and as they give us the precious static, this it is when the keys are closed so the output velocity is zero, v₂= 0. The height of the floors in a building is y₂ = 12 m

we substitute in Bernoulli's equation

P_{atm} + 0 + ρ g h = P₂ + 0 + ρ g y₂

h =
`((P_2 - P_(atm)) + \rho \ g \ y_2)/(\rho \ g)`

h =
`(\Delta P)/(\rho g)` + y₂

indicate that the value of ΔP = 410 10³ Pa

we calculate

h = 410 10³ / (1000 9.8) + 12

h = 53.8 m

b) ask for the height range for the minimum and maximum pressure

h =
`(\Delta P)/(\rho g)` ΔP / rho g

minimum

h_minimum = 275 103/1000 9.8

h_minimum = 28 m

maximums

h_maximo = 620 103/1000 9.8

h_maximum = 63.3 m