Question

A 0.5 cm diameter, 50 cm long horizontal tube is connected to a beaker containing n-butyl alcohol with the orifice located 10 cm below the surface.   Alcohol(70 degrees F) exits from the tube and drops into another container.    Predict the volumetric flow rate for this system. What is the error if the Bernoulli equation is used?

Answer 1

The above diagram shows the situation given the problem and assume figure is not to the scale. The tank contains the n-butyl alcohol at 70 F almost  C where n-butyl alcohol in the stable condition.

The friction factor is not given the problem, we assume it = 0.009 for a pipe

Let d= 0.5 cm = 0.005m

L= 50 cm = 0.5 m

H= 10 cm = 0.1 m

= friction factor = 0.009

V= velocity of n-butyl alcohol in the pipe m/s

Generally this kind of problems are solve by bernoullis equation only and error associated with the equation and performing experiment on lab and doing calculation is around 10 %.

Applying Bernoullis eqaution at the top of the butyl alcohol surface in the tank and at the outlet of pipe, we have [Taking point 1 on the top and point 2 at the outlet of the pipe]

Considering datum line passing through centerline of pipe

0+0+0.1 = 0+ +0 + ( )

or 0.1 =   + ( )

But the velocity in the pipe = V   V= V₂

Where, the h_i is loss of head at the entrance of the pipe and is given by formula

and h_f is the loss of head due the friction and is given by

Substituing these values, we have

0.1 =

=  

=

  

Rate of flow =