Water enters a house through a pipe 2.40 cm in diameter, at an absolute pressure of 4.10 atm. The pipe leading to the second floor bathroom, 5.20 m above, is 1.20 cm in diameter. The flow speed at the inlet pipe is 4.75 m/s. a) What is the algebraic expression for flow speed in the bathroom? b) Calculate the flow speed in the bathroom. c) What is algebraic expression for the pressure in the bathroom? d) Calculate the water pressure in the bathroom. Report your answer in the (atm) unit.

We shall apply theory volume conservation to calculate rate of flow of water.

a) A₁ V₁ = A₂V₂, A₁ and A₂ are area of cross section and V₁, V₂ are velocity of flow at two places along pipe.

b) π x 1.2² x 4.75 = π x 0.6² x V₂

V₂ = 4 X 4.75

= 19 m / s

c)

For finding pressure we shall apply Bernoulli's theorem

P₁ + 1 / 2 ρ v₁² = P₂ + 1 / 2 ρ v₂² + (h₂ - h₁) ρ g

P₁ and P₂ are pressure at ground and second floor, v₁ and v₂ are velocity at two floors and h₁, h₂ are height of two floors. ρ is density of water.

4.1 x 10⁵ + 1/2 x 1000 x 4.75² = P₂ + 1/2 x 1000 x 19² + 5.2 x 1000 x 9.8

4.1 x 10⁵ +.11 x 10⁵ = P₂ + 1.8 X 10⁵ +.51 X 10⁵

P₂ = 1.9 X 10⁵

= 1.9 atm.