Question

Water flows at 0.20 L/s through a 12-m-long garden hose 2.5 cm in diameter that is lying flat on the ground. The temperature of the water is 20 ∘C.

What is the gauge pressure of the water where it enters the hose?

Answer 1

The water flow rate

Q = 0.20 L / s

Q = 0.20 [ 1000 cm^3] / s

Q = ( 0.20 ) [ 10^3 ( 10^-2 m )^3 ³ ] / s

Q = 0.20 X 10^-3 m^3 / s
The pressure drop is given by

Δp = 8 μ L Q / [ π r^4 ]

= 8 μ L Q / [ π ( 1/2 d )^4 ]

= 8 μ L Q / [ π d^4 / 16 ]

= 8 ( 16 ) μ L Q / [ π d^4 ]

At 20°μ = 1.002 × 10^-3 Pa*s

8( 16 ) μ L Q = 128 μ L Q

= 128 ( 1.002 x 10^-3 Pa*s ) ( 12 m ) ( 0.20 x 10^-3 m^3 / s )

= 3.078 x 10^-4 N.m^2

Δp = 8 ( 16 ) μ L Q / [ π d^4 ]

= ( 3.078 x 10^-4 N.m^2 ) / [ π ( 2.5 x 10^-2 m )^4 ]

= 250.830 Pa pressure drop

Gauge pressure Δp = - 250.830 Pa