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

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Answer 1 · 2018-04-22T01:30:56

#"7.5 s"#

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"#