Problem 1.33

# Problem 1.33 - c 2.38 R 1 2 in 2 ⋅ s ⋅ ft 3 ⋅ = For...

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Problem 1.33 [Difficulty: 2] Given: Equation for maximum flow rate. Find: Whether it is dimensionally correct. If not, find units of 2.38 coefficient. Write a SI version of the equation Solution: Rearrange equation to check units of 0.04 term. Then use conversions from Table G.2 or other sources (e.g., Google) "Solving" the equation for the constant 2.38: 2.38 m max T 0 A t p 0 = Substituting the units of the terms on the right, the units of the constant are slug s R 1 2 × 1 ft 2 × 1 psi × slug s R 1 2 × 1 ft 2 × in 2 lbf × lbf s 2 slug ft × = R 1 2 in 2 s ft 3 = Hence the constant is actually
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Unformatted text preview: c 2.38 R 1 2 in 2 ⋅ s ⋅ ft 3 ⋅ = For BG units we could start with the equation and convert each term (e.g., A t ), and combine the result into a new constant, or simply convert c directly: c 2.38 R 1 2 in 2 ⋅ s ⋅ ft 3 ⋅ = 2.38 R 1 2 in 2 ⋅ s ⋅ ft 3 ⋅ K 1.8 R ⋅ ⎛ ⎝ ⎞ ⎠ 1 2 × 1 ft ⋅ 12 in ⋅ ⎛ ⎝ ⎞ ⎠ 2 × 1 ft ⋅ 0.3048m ⋅ × = c 0.04 K 1 2 s ⋅ m ⋅ = so m max 0.04 A t p ⋅ T ⋅ = with A t in m 2 , p in Pa, and T in K....
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