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To determine the venturi dimensions and expected differential pressure reading for air flow at 50000 Reynolds number, 500 kPa and 50°C, through a circular tube with 50 mm diameter, we can use the following steps:
- Calculate the air velocity in the circular tube:
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The flow rate (Q) can be calculated using the formula Q = π*(d^2)/4 * v, where d is the diameter of the tube and v is the air velocity.
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Rearranging the formula, we can get v = (4*Q)/(π*d^2).
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Substituting the given values, we get v = (4*0.0196)/(π*0.05^2) = 12.56 m/s.
- Calculate the diameter of the throat:
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The Reynolds number (Re) can be calculated using the formula Re = (ρvd)/μ, where ρ is the density of air, μ is the dynamic viscosity of air, and all other variables are as previously defined.
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Rearranging the formula, we can get d = (Re*μ)/(ρ*v).
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Substituting the given values, we get Re = (ρvd)/μ => d = (Re*μ)/(ρv) = (500000.0000185)/(1.184*12.56) = 0.0037 m.
- Calculate the diameter of the inlet:
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The area ratio (A1/A2) of the inlet to the throat can be calculated using the formula A1/A2 = (1/ε)^2 * ((2/(γ+1))^((γ+1)/(γ-1)) / ((γ+2)/(γ-1))^((γ+2)/(γ-1))), where ε is the contraction coefficient, γ is the specific heat ratio of air, and all other variables are as previously defined.
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Substituting the given values, we get A1/A2 = (1/0.6)^2 * ((2/1.4)^1.4 / (4.4/1.4)^2.2) = 2.21.
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Since the area of the throat is known (πd^2/4), we can calculate the area of the inlet by multiplying it with the area ratio: A1 = A2 * A1/A2 = π(0.0037^2)/4 * 2.21 = 8.40E-06 m^2.
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The diameter of the inlet can be calculated using the formula d = 2*sqrt(A1/π) = 0.00293 m.
- Calculate the expected differential pressure reading:
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The differential pressure (ΔP) can be calculated using the formula ΔP = (ρ*v^2/2) * ((A2/A1)^2 - 1), where all variables are as previously defined.
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Substituting the given values and the calculated values from steps 2 and 3, we get ΔP = (1.184*12.56^2/2) * ((0.0037/0.00293)^2 - 1) = 525.8 Pa.
Therefore, the venturi dimensions for air flow at 50000 Reynolds number, 500 kPa and 50°C, through a circular tube with 50 mm diameter are: the diameter of the throat is 0.0037 m and the diameter of the inlet is 0.00293 m. The expected differential pressure reading is 525.8 Pa.
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