## what is thrust force?

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Yanda.Jiang
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Joined: Sun Mar 10, 2019 7:44 pm
Organization: Iowa state university
Location: United States

### what is thrust force?

Hi guys,

While learning betz's law, I notice thrust forces at the inlet and outlet of control volume are both represented as density*area*velocity^2, which is different from thrust force caused by air pressure difference at the two sides of turbine itself, since air pressure at inlet and outlet of control volume are same while thrust forces at inlet and outlet are different.
As far as I know, thrust force represents force that changes air flow momentum (plz correct me if I am wrong), but after searching on google for a long time, I still don't know clearly what it is in essence if it is not related to air pressure difference.
Kindly let me know your thoughts. Many thx
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Best regards,
Yanda

Jason.Jonkman
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### Re: what is thrust force?

Dear Yanda,

There are not different thrust forces at the inlet and outlet of the control volume. Instead, the thrust force of the rotor can be written as the difference in linear momentum between the inlet and outlet, i.e.,

T = rho*S_1*V_1^2 - rho*S_2*V_2^2,

or equivalently from Bernoulli's equation,

T = 1/2*rho*S*(V_1^2 - V_2^2),

using your nomenclature. This thrust force is equivalent to the pressure difference between the upwind and downwind sides of the rotor.

I hope that helps.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Yanda.Jiang
Posts: 16
Joined: Sun Mar 10, 2019 7:44 pm
Organization: Iowa state university
Location: United States

### Re: what is thrust force?

Jason.Jonkman wrote:Dear Yanda,

There are not different thrust forces at the inlet and outlet of the control volume. Instead, the thrust force of the rotor can be written as the difference in linear momentum between the inlet and outlet, i.e.,

T = rho*S_1*V_1^2 - rho*S_2*V_2^2,

or equivalently from Bernoulli's equation,

T = 1/2*rho*S*(V_1^2 - V_2^2),

using your nomenclature. This thrust force is equivalent to the pressure difference between the upwind and downwind sides of the rotor.

I hope that helps.

Best regards,

Dear Jason,

Thx for your prompt and accurate reply. I finally understand it. I love your response soooooo much.

Best,
Yanda

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