Question

How long it will take for 500ml of water to flow through a 15cm long 1.5mm radius if the pressure differential across the pipe is 4kpa?the viscosity of water is 0.8 cpoise. Ans=7.5s

please helpppp

Answer 1

`"7.5 s"`

Explanation:

Convert everything into `"C.G.S"` units

• `"V = 500 mL = 500 cm"^3`

• `l = "15 cm"`

• `"r = 1.5 mm = 0.15 cm" color(white)(..)[∵ "1 mm = 0.1 cm"]`

• `Δ"P = 4 kPa = 4" × 10^3\ "Pa" = 4 × 10^4\ "dyne/cm"^2`
  `[∵ "1 Pa = 1 N/m"^2 = "10 dyne/cm"^2]`

• `eta = "0.8 cpoise" = 0.8 × 10^-2\ "poise"`
  `color(white)(..)[∵ "1 cpoise" = 10^-2\ "poise"]`

Volume of water per unit time is

`"V"/t = ("ΔPπr"^4)/(8 eta l)`

`t = (8"V" eta l)/("ΔPπr"^4) = (8 × "500 cm"^3 × 0.8 × 10^-2\ "poise" × "15 cm")/(4 × 10^4\ "dyne/cm"^2 × 3.14 × ("0.15 cm")^4)`

`t = 7.5\ "s"`