Water enters a house at 1.5 m/s through a pipe with an inside radius of 1.0cm and at a pressure of 400,000 pa. the water then travels up 5.0 m to a second floor bathroom through a pipe of radius 0.5 cm. calculate the pressure of the water (in pa) when it reaches the bathroom.( we have not covered yetthe concept for this problem)

pressure of the water = 3.3 × pa

Explanation:

given data

velocity v1 = 1.5 m/s

pressure P = 400,000 Pa

inside radius r1 = 1.00 cm

pipe radius r2 = 0.5 cm  

h1 = 0 (datum at inlet)

h2 = 5.0 m (datum at inlet)

density of water ρ = 1000 kg/m³

to find out

pressure of the water

solution

we consider here flow speed in bathroom that is =  v2 and Pressure in bathroom is =  P2  

here we will use both continuity and Bernoulli equations

because here we have more than one unknown so that  

v1 × A1 = v2 × A2 × P1 +  ρ g h1 + (0.5)ρ v1² = P2 + ρ g h2 + (0.5) ρ v2²

now we use here first continuity equation for get v2

v2 =    

v2 =    

v2 = 6 m/s

and now we use here bernoulli eqution for find here p2 that is

P2 = P1 - 0.5× ρ ×(v2² - v1²) - ρ g (h2- h1 )

P2 = 400000  - 0.5× 1000 ×(6² - 1.5²) - 1000 × 9.81 × (5-0 )

P2 = 3.3 × pa

the correct choice is a .

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