Your company is planning to build a pipeline to transport gasoline from the refinery to a field of storage tanks. The parameters for the prototype system are a pipe diameter of 1 m, with a flow velocity of 0.5 m/s at 25°C. The model system will use water at STP with a geometric scaling factor of 1 : 20. What fluid velocity is required in the model system to guarantee kinematic similarity in the form of equal Reynolds numbers?

Answers

Answer 1

Answer:

The model system will need water flowing at a velocity of 2.07 meters per second to guarantee kinematic similarity in the form of equal Reynolds numbers.

Explanation:

The Reynolds number ([tex]Re_{D}[/tex]) is a dimensionless criterion use for flow regime of fluids, which is defined as:

[tex]Re_{D} = \frac{\rho \cdot v\cdot D}{\mu}[/tex] (Eq. 1)

Where:

[tex]\rho[/tex] - Density, measured in kilograms per cubic meter.

[tex]\mu[/tex] - Dynamic viscosity, measured in kilograms per meter-second.

[tex]v[/tex] - Average flow velocity, measured in meters per second.

[tex]D[/tex] - Pipe diameter, measured in meters.

We need to find the equivalent velocity of water used in the prototype system. In this case, we assume that [tex]Re_{D,gas} = Re_{D,w}[/tex]. That is:

[tex]\frac{\rho_{w}\cdot v_{w}\cdot D_{w}}{\mu_{w}} = \frac{\rho_{gas}\cdot v_{gas}\cdot D_{gas}}{\mu_{gas}}[/tex] (Eq. 2)

Where subindex [tex]w[/tex] is used for water and [tex]gas[/tex] for gasoline.

If we know that [tex]\rho_{gas} = 690\,\frac{kg}{m^{2}}[/tex], [tex]\mu_{gas} = 0.006\,\frac{kg}{m\cdot s}[/tex], [tex]v_{gas} = 0.5\,\frac{m}{s}[/tex], [tex]D_{gas} = 1\,m[/tex], [tex]\rho_{w} = 1000\,\frac{kg}{m^{3}}[/tex], [tex]\mu_{w} = 0.0018\,\frac{kg}{m\cdot s}[/tex] and [tex]D_{w} = 0.05\,m[/tex], then we get the following formula:

[tex]57500 = 27777.778\cdot v_{w}[/tex]

The fluid velocity for the prototype system is:

[tex]v_{w} = 2.07\,\frac{m}{y}[/tex]

The model system will need water flowing at a velocity of 2.07 meters per second to guarantee kinematic similarity in the form of equal Reynolds numbers.


Related Questions

Nicole designs the hardware configuration of workstations that will be deployed to a newly formed company. She sets up the networking capabilities and policies that will govern the workstations when connected to the company network. What is her role in her company?

Answers

Answer:

a Network Engineer (architect)

Explanation:

Indeed, as a Network Engineer, we would expect Nicole to be in charge of planning, setting up, and managing the software and hardware components of the computer networks so that they function as intended.

A Network Engineer therefore would be responsible for setting up the networking capabilities and policies that will govern the workstations when connected to the company network.

Facts about cellphones

Answers

Answer:

Your mobile phone has more computing power than the computers used for the Apollo 11 moon landing.

Mobile phones have to “work harder” to get a signal if you are in a moving vehicle.

The first mobile phone was made in 1973.

The first mobile phones that went on sale in 1983 cost nearly $4,000 each.

In 2012 Apple sold 340,000 phones per day.

4 out of 10 Brits admit to snooping on their partners phone.

Out of the 53% of snoopers that found incriminating evidence on their partner’s phone, 5% went on to terminate their relationship.

Waterproof mobile phones came to market because Japanese youngsters like to use them in the shower.

Apparently mobile phones have 18 times more bacteria on them than toilet handles!

Phubbing describes the act of snubbing someone by using your mobile phone in their company.

In 2015 more people died from taking selfies than shark attacks.

Teenagers that use a phone more than 2 hours a day increase their risk of depression and anxiety.

Nomobophobia is severe anxiety caused by the thought or act of losing your phone or running out of battery.

Explanation:

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