Question 11.SP.6: Determine the weight flow rate when air at 20°C and 700kN/m²......
Determine the weight flow rate when air at 20°C and 700kN/m² abs flows through a venturi meter if the pressure at the throat of the meter is 400kN/m² abs. The diameters at inlet and throat are 250 and 125 mm, respectively. Assume that C=0.985.
p_{2} / p_{1}=\frac{400}{700}=0.571 ; D_{2} / D_{1}=0.50. Fig. 11.25: \quad Y \approx 0.72
Eq. (2.5): \quad \gamma_{1}=\frac{g p}{R T}=\frac{\left(9.81 \mathrm{~m} / \mathrm{s}^{2}\right)\left(700 \mathrm{kN} / \mathrm{m}^{2}\right)}{\left[287 \mathrm{~m}^{2} /\left(\mathrm{s}^{2} \cdot \mathrm{K}\right)\right](273+20) \mathrm{K}}=0.0817 \mathrm{kN} / \mathrm{m}^{3}
Eq. (11.23): \quad G=0.985(0.72) \frac{\pi(0.125)^{2}}{4} \sqrt{2(9.81) 0.0817 \frac{700-400}{1-(0.5)^{4}}}
G=0.1971 \mathrm{kN} / \mathrm{s}=197.1 \mathrm{~N} / \mathrm{s}If the relation between C and \mathbf{R}_{2} for this meter is known, the value of \mathbf{R}_{2} for the computed value of G can be determined. If the assumed value of C does not correspond with this value of \mathbf{R}_{2}, a slight adjustment in the value of C can be made to give a more accurate answer.
g \dot{m}=G=C Y A_2 \sqrt{2 g \gamma_1 \frac{p_1-p_2}{1-\left(D_2 / D_1\right)^4}} (11.23)
\gamma=\frac{g p}{R T} (2.5)
