Question

Air at 20°C and 1 atm flows at 50 ft/s past a thin flat plate whose area (bl) is 24 ft^2. If the total friction drag is 0.3 lbf, what are the length and width of the plate?

Answer 1

The length is 1.36 feet and the breadth is  17.647 feet of the plate, if friction drag is 0.3 lbf.

T = 20°C = 293 K

P = 1 atm = 101.325kP

P = ρRT

ρ = 1.205 kg/m³

Total drag = C∝ * (1/2 .ρ . A . V²)

0.3 lbf = C∝ * 1/2 * 1.205 * 4.645 * (15.24)²

    C∝ = 2.05338 * 10 ⁻³

Now,

          C∝ = 1.328 / √Re

        2.05338 * 10 ⁻³ = 1.328 / √Re

∴ Re = 418267.61

∴  ρ. v. l/μ = 418267.61

1.205 * 15.24 *L/18.207 * 10⁻⁶ =  418267.61

    Length  = 0.4147 m = 1.36 foot

L * B = 24 ft²

1.36 * B = 24

∴ breadth = 17.647

Hence, Length is 1.36 feet and the breadth is  17.647 foot.

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