Question

The water flows from a tap of diameter 1.25 cm with a rate of $5\times {10}^{-5}{m}^3{s}^{-1}.$ The density and coefficient of viscosity are ${10}^{3}kg{m}^{3}and{10}^{-3}$ Pa_s respectively. The flow of water is

• A. steady with Reynolds number 5100
• B. turbulent with Reynolds number 5100
• C. steady with Reynolds number 3900
• D. turbulent with Reynolds number 3900

Answer 1

The correct option is B turbulent with Reynolds number 5100

Reynolds number,
$R_e=\frac{v\rho D}{\eta }andv=\frac{4Q}{\pi D^2}(asQ=\frac{\pi D^2}{4}v),R_e=\frac{4Q\rho }{\pi d\eta }Here,D=1.25cm=1.25\times {10}^{-2}mP={10}^{3}kg{m}^{-3},\eta ={10}^{-3}PasQ=5\times {10}^{-5}{m}^3{s}^{-1}{R}_e=\frac{4\times 5\times {10}^{-5}\times {10}^3}{3.14\times 1.25\times {10}^{-2}\times {10}^{-3}}=5095\approx 5100.For{R}_e>3000,$ the flow is turblent.