6506-5 - s 2/C- 1/r c 2/C ) (Eq. 4) r c r s Substituting...

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1 BROOKFIELD ROTATIONAL VISCOMETER (AASHTO T 48 , ASTM D 4402) Rotational Viscometer
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2 Rotational Viscometer Rotational Viscometer (RV) sample chamber spindle asphalt sample applied torque from motor, T angular velocity, w
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3 BROOKFIELD ROTATIONAL VISCOMETER FUNDAMETALS Shear Stress, τ = F / A Shear Force, F = T / r s A = Area at the surface of the spindle = 2 π r s L L = Effective length of the spindle Shear stress at the surface of the spindle: τ = T / (2 π r 2 L) (Eq. 1) Shear rate between two plates: d γ /dt = r d ω / dr (Eq. 2) Where r = radius where the shear rate is determined d ω = difference in rotational speed over the thickness dr, in radians/second
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4 According to Power Law Equation τ = η 0 (d γ /dt) C (Eq. 3) T / (2 π r 2 L) = η 0 (r d ω /dr) C r d ω /dr = (T/2 η 0 π r 2 L) 1/C d ω = (T/2 η 0 π L) 1/C (1/r 1+2/C ) dr ⇒∫ d ω = (T/2 η 0 π L) 1/C (1/r 1+2/C ) dr ⇒ω = (T/2 η 0 π L) 1/C (C/2) ( 1/r
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Unformatted text preview: s 2/C- 1/r c 2/C ) (Eq. 4) r c r s Substituting Eq. 1 into Eq. 3 gives: d /dt = (T/2 0 L) 1/C (1/r 2/C ) (Eq. 5) Substituting Eq. 5 into Eq. 4 gives: = (d /dt) r 2/C (C/2) ( 1/r s 2/C- 1/r c 2/C ) Re-arranging d /dt = 2 /(C ( 1/r s 2/C- 1/r c 2/C ) r 2/C ) = 2 r s 2/C r c 2/C /(C(r c 2/C- r s 2/C ) r 2/C ) 5 At the surface of the spindle r = r s The shear rate can be calculated as: d /dt = 2 r c 2/C /(C(r c 2/C- r s 2/C )) For a Newtonian fluid, C = 1 d /dt = 2 r c 2 /(r c 2- r s 2 ) (Eq. 6) The Brookfield software uses Equ. 6 to compute the shear rate, d /dt . By definition, Viscosity, = / (d /dt) Substituting Eq. 1 and Eq. 6 into above = T(r c 2- r s 2 ) / 4 r c 2 r s 2 L The above equation is only valid for a Newtonian fluid....
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6506-5 - s 2/C- 1/r c 2/C ) (Eq. 4) r c r s Substituting...

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