Fluids...Any help is appreciated..Thanks!?

Question

The fluid in the tank is gasoline. The top of the fluid in the tank is 13.5 meters above the exit pipe. The pipe is 3 inch schedule 40 iron pipe and the nozzle ¾ inch schedule 40 pipe. Find the discharge velocity and the pressure at point D in the pipe.

Area of 3/4" pipe=3.437*10^-4m^2

Area of 3" pipe=4.768*10^-3m^2

Answer 1

First calculate the hydrostatic head from the gasoline

Density of gasoline is approx 0.784 gm/cm3- from wikipedia

I am going to convert to kg/m3... you can use different units

0.784 gm/cm3 * 1kg/1000gms * 1000cm3/m3= 0.784 kg/m3

Hydrostatic head= 0.784 kg/m3 * 13.5m= 105.8 kg/m2

this is the pressure in the 3 in pipe.

You didn't say where point D is located.

In any event you will have to calculate the velocity at the 3/4 pipe. There is a formula, that I don't recall, since I do not have my reference book here, that relates pressure drop to velocity

The pressure drop across the 3/4 pipe is 105.8 kg/m2 on the inlet side and 0 kg/m2 on the outlet side. (this is using gauge units. you can convert to absolute units if needed by adding the atmospheric pressure (14.7 psi) in kg/m2 units.

Refer to your text book to get the proper formula... look for Bernoulli's principle.

Here is the formula

The original form of Bernoulli's equation[3] is:

V^2/2 + gh + p/rho = constant



where:

v is the fluid velocity at a point on a streamline

g is the acceleration due to gravity

his the height of the point above a reference plane

p is the pressure at the point

rho is the density of the fluid at all points in the fluid

The following assumptions must be met for the equation to apply:

The fluid must be incompressible - even though pressure varies, the density must remain constant.

The streamline must not enter the boundary layer. (Bernoulli's equation is not applicable where there are viscous forces, such as in the boundary layer.)