Question

A straight horizontal garden hose 49.0 m long with an interior diameter of 1.30 cm) is used to deliver 20C water at the rate of 0.490 liters/s. Assuming that Poiseuille's Law applies, estimate the pressure drop (in Pa) from one end of the hose to the other.

Answer 1

According to Poiseuille's Law, P = 128 L Q / (d⁴⁾

where,

is the dynamic viscosity = 1.002 10^-3 Pa s.

(The dynamic viscosity of water at 20 C is 1.002 x 10^-3 Pa s)

L is the length of the circular hose = 49 m

d is the diameter = 1.30 cm = 1.30 x 10^-2 m

Q is the volumetric flow rate = 0.490 lit/s

= 4.90 x 10^-4 m³/s ( because, 1 lit/s = 10^-3 m³/s)

P = 128 L Q / (d⁴)

= (128 * 1.002 10^-3 Pa s * 49 m * 4.90 x 10^-4 m³/s) / ( * (1.30 x 10^-2)⁴)

= 3432.64 * 10

= 34326.4 Pa