Question

A pipe transporting a fluid has an internal diameter of 5.0 m. The fluid has a flow rate of 5.00 × 10−2 m3 /s and a viscosity of 1.00 × 10−3 N/m2 ∙s. The fluid has a density of 695 kg/m3 and a pressure of 1.62 × 104 Pa. Consider the fluid to be ideal. a) Calculate the speed of the fluid in the pipe. b) What is the maximum diameter that the pipe must have if the flow is to be laminar? c) The pipeline rises 10 m into a secondary pipe of internal diameter 2.4 m. What is the new pressure of the fluid in the secondary pipe? d) Under what flow conditions would you expect to have as little energy losses as possible when transporting the fluid? Clearly justify your response.

Answer 1

(a) The velocity of the fluid can be calculated using the formula, where v is the velocity of the fluid, Q is the flow rate and A is the cross sectional area of the pipe.

Therefore

(b) In order for the flow to be laminar, the velocity of the fluid must be less than the critical velocity. In order to know if the flow of liquid is laminar or not, we must calculate the Reynold's number.

Reynold's no.= where is the fluid density, v is the fluid velocity, d is the internal diameter of the pipe and is the fluid viscosity.

Since the reynold's number is greater than 2900, the flow is not laminar. We need to find the critical velocity. the flow is laminar when the reynold's number is below 2300.

Therefore,

The cross sectional area of the pipe should be

Hence the maximum diameter of the pipe can be,

(c) The Bernoulli equation is

P1=, , V1=, h1=0, g=9.8m/s, P2=?,

So by Bernoulli equation

(d) In order to minimise energy losses, the fluid must flow at a constant depth, i.e. h1=h2.