A rotameter calibrated for metering has a scale ranging from 0.014 m3/min to 0.14 m3/min. It is intended to use this meter for metering a gas of density 1.3 kg/m3 with in a flow range of 0.028 m3/min to 0.28 m3/min. What should be the density of the new float if the original one has a density of 1900 kg/m3? Both the floats can be assumed to have the same volume and shape
.Data:
Old:
Density of float (
ρf)= 1900 kg/m3Density of gas (ρ) = 1.3 kg/m3
Qmin = 0.014 m3/min
New:
Density of gas (ρ) = 1.3 kg/m3
Qmin = 0.028 m3/min
Formula:
\(\displaystyle Q = C_D A_2\sqrt{\frac{2V_f(\rho_f-\rho)g}{\rho A_f\bigl(1-(A_2/A_1)^2\bigr)}}\)
Where Q = volumetric flow rate
A2 = area of annulus (area between the pipe and the float)
A1 = area of pipe
Af = area of float
Vf = volume of float
CD = rotameter coefficient
Calculations:
From the equation, for the same float area and float volume and the pipe geometry,
Q = k (ρf - ρ)0.5
where k is a proportionality constant
Qnew / Qold = ( (ρfnew - ρ) / (ρfold - ρ) )0.5
i.e. 0.028 / 0 .014 = ( (ρfnew - 1.3) / (1900 - 1.3) )0.5
2 = (ρfnew - 1.3)0.5 / 43.574
(ρfnew - 1.3)0.5 = 87.15
(ρfnew - 1.3) = 7595.1
ρfnew = 7596 kg/m3
Last Modified on: 01-May-2024
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