Question

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)

Answer 1

Answer:

pressure of the water = 3.3 × $10^{5}$ 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 = $v1 \frac{A1}{A2}$    

v2 = $1.5 \frac{\pi * 0.01^2}{\pi * 0.005^2}$    

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 × $10^{5}$ pa