Carbon dioxide flows at a rate of 1.5 ft3 /s from a 3-in. pipe in which the pressure and temperature are 20 psi (gage) and 120 °F into a 1.5-in. pipe. If viscous effects are neglected and incompressible conditions are assumed, determine the pressure in the smaller pipe

the absolute pressure in the smaller pipe = 19.63 psi

Explanation:

Let A be the diameter of the first pipe = 3 inches

Let B be the diameter of the second pipe.  = 1.5 inches

To feet (ft) ; we have

Diameter of the pipe A

Diameter of pipe B  

Temperature T = 120° F = (120+ 460)°R

= 580 ° R

The pressure gage to atmospheric pressure ; we have:

where;

atmospheric pressure = 1.47 psi

pressure gage = 20 psi

To lb/ft²; we have:

4.998.6 fb/ft²

The density of carbon dioxide can be calculated by using the relation

Formula for calculating cross sectional area is

For diameter of pipe

A₁ =

A₁ = 0.04909 ft²

For diameter of pipe

A₂

A₂ = 0.012227 ft²

Using the continuity equation to determine the velocities V₁ and V₂ respectively.

For V₁

Q = A₁V₁

V₁ = Q₁/ A₁

V₁ = 1.5/0.04909

V₁ = 30.557 ft/s

For V₂

Q = A₂V₂

V₂= Q₂/ A₂

V₂ = 1.5/0.04909

V₂ = 30.557 ft/s

Finally; using Bernoulli's Equation to the flow of the carbon dioxide from the larger pipe to the smaller pipe ; we have:

Since the pipe is horizontal then;

So;

To psi;

gage

The absolute pressure in the smaller pipe can be calculated as:

Hence, the absolute pressure in the smaller pipe = 19.63 psi

the clapeyron equation (also called the clausius-clapeyron equation) relates the slope of a reaction line on a phase diagram to fundamental thermodynamic properties.

explanation: