Water at 20^(@)Cis flowing in a horizontal pipe that is 20.0m long.The flow is laminar and the water completely fills the pipe. A pump maintains a gauge pressure of 1400Pa, at a large tank at one end of the pipe. The other end of the pipe is open to the air, The viscosity of water at 20^(@)C is 1.005 poise (a) If the pipe has diameter 8.0 cm, what is the volume flow rate? (b) What gauge pressure must the pump provide to achieve the same volume flow rate for a pipe with a diameter of 4.0cm? (c) For pipe in part (a) and the same gauge pressure maintained by the pump, what does the volume flow rate become if the water is at a temperature of 60^(@)C (the viscosity of water at 60^(@)C is 0.469 poise?

Water at 20^(@)Cis flowing in a horizontal pipe that is 20.0m long.The

1.	Water at 20^(@)Cis flowing in a horizontal pipe that is 20.0m long.The flow is laminar and the water completely fills the pipe. A pump maintains a gauge pressure of 1400Pa, at a large tank at one end of the pipe. The other end of the pipe is open to the air, The viscosity of water at 20^(@)C is 1.005 poise (a) If the pipe has diameter 8.0 cm, what is the volume flow rate? (b) What gauge pressure must the pump provide to achieve the same volume flow rate for a pipe with a diameter of 4.0cm? (c) For pipe in part (a) and the same gauge pressure maintained by the pump, what does the volume flow rate become if the water is at a temperature of 60^(@)C (the viscosity of water at 60^(@)C is 0.469 poise?
Answer» Solution :(a) `Q=(pi)/(8)((R^4)/(eta))((p_(1)-p_(2))/(L))` `=((pi)/(8))((0.04)^(4))/(1.005xx10^(-1))xx(1400)/(0.2)` `=7xx10^(-2)m^(3)//s`. (b) `Q_(1)=Q_(2)` `:. [(p_(1)-p_(2))R^(4)]_(i)=[(p_(1)-p_(2))R^(4)]_(F)` Since, diameter or radius has decreased to half. Therefore gauge pressure should become 16 times or, `(p_(1)-p_(2))_(f)=16xx1400` `=2.24xx10^(4)Pa` (C )`Q prop (1)/(eta)` `:. (Q_1)/(Q_2)=(eta_2)/(eta_1)` or, `Q_(2)=((eta_(1))/(eta_(2)))Q_(1)` `=((1.005)/(0.469))(7xx10^(-2))` `=0.15m^(3)//s`.