Question

Air at 80 °F is to flow through a 72 ft diameter pipe at an average velocity of 34 ft/s . What diameter pipe should be used to move water at 60 °F and average velocity of 71 ft/s if Reynolds number similarity is enforced? The kinematic viscosity of air at 80 °F is 1.69E-4 ft^2/s and the kinematic viscosity of water at 60 °F is 1.21E-5 ft^2/s. Round your answer (in ft) to TWO decimal places.

Answer 1

2.47 ft

Step-by-step explanation:

Given that:

The initial temperature of air = 80°F

Diameter of the pipe = 72 ft

average velocity of the air flow through the pipe = 34 ft/s

The objective is to determine the diameter of the pipe to be used to move water at:

At a temperature = 60°F &

An average velocity of 71 ft/s

Assuming Reynolds number similarity is enforced;

where :

kinematic viscosity (V_air) of air at 80 °F (V_air) = 1.69 × 10⁻⁴ ft²/s

kinematic viscosity of water at 60 °F (V_water) = 1.21 × 10⁻⁵ ft²/s

The diameter of the pipe can be calculated by using the expression:

2.4686 ft

2.47 ft ( to two decimal places)

Thus; diameter pipe to be use to move water at the given temperature and average velocity is 2.47 ft

Answer 2

2.47 ft

Step-by-step explanation:

Given that:

The initial temperature of air = 80°F

Diameter of the pipe = 72 ft

average velocity
`v_(air)` of the air flow through the pipe = 34 ft/s

The objective is to determine the diameter of the pipe to be used to move water at:

At a temperature = 60°F &

An average velocity
`v_(water)` of 71 ft/s

Assuming Reynolds number similarity is enforced;

where :

kinematic viscosity (V_air) of air at 80 °F (V_air) = 1.69 × 10⁻⁴ ft²/s

kinematic viscosity of water at 60 °F (V_water) = 1.21 × 10⁻⁵ ft²/s

The diameter of the pipe can be calculated by using the expression:

`D_(water) = (V_(water))/(V_(air))*(v_(air))/(v_(water))* D_(air)`

`D_(water) = (1.21*10^(-5) \ ft^2/s)/(1.69*10^(-4) \ ft^2/s)*(34 \ ft/s)/(71 \ ft/s)* 72 \ ft`

`D_(water) =` 2.4686 ft

`D_(water) =` 2.47 ft ( to two decimal places)

Thus; diameter pipe to be use to move water at the given temperature and average velocity is 2.47 ft