Pengembangan Proses : Peningkatan skala Dr. Erliza Noor

1. Pengembangan Proses : Peningkatan skala Dr. Erliza Noor

2. Meliputi rancang bangun • Konstruksi • Proses operasi peralatan skala besar dari data percobaan Cakupan dalam Peningkatan Skala

3. Kriteria dalam peningkatan skala • Kesamaan tenaga per unit volume • Nilai tenaga per unit volume untuk skala besar harus berada diatas nilai batas yang ditentukan • Koefisien Transfer Oksigen : Korelasi empiris yang menghubungkan koefisien transfer oksigen keseluruhan dengan variabel-variabel peralatan dan operasi.

4. Persyaratan Penggandaan skala • Geometri sistem sama • Bahan yang digunakan sama • Proporsi bahan sama

5. Pendekatan Penggandaan skala • Analisa tak berdimensi • Contoh untuk pencampuran • Pm/Pl = (Dl/Dm)3 • m : model • l : prototipe skala besar • Pl/Dl3 = Pm/Dm3

6. Analisis Dimensional • Merupakan salah satu teknik untuk peningkatan skala selain dengan cara trial and error, metode dasar (perpindahan massa, panas dan momentum), metode semi dasar (neraca yang disederhanakan) • Teknik menggunakan gugus nirmatra ( tak berdimensi) sebagai parameter dalam rancang bangun

7. Analisis Dimensional • Neraca mikro dapat merampatkan (generalisasi) gugus nirmatra suatu parameter • Gugus parameter al • - Parameter geometri : D, H, dp • - Sifat (padatan, gas) :μ, ρ • - Peubah proses : N, P, V • - tetapan bermatra : g, R • Besaran yang sering digunakan adalah : massa, panjang, waktu dan suhu.

9. Design of membrane processes Prediction of Mass Transfer Coefficients The equation used, depend on the flow regime-calculated using “Reynolds number” Turbulent Flow (RE > 10.000) The equation used, depend on the flow regime-calculated using “Reynolds number” Where : Schimid no. Dh = Equivalent Hydraulic Diameter D = Diffusitivity

10. Laminar Flow (RE < 1000) L = Channel Length

11. Problem 1 Liquid is flowing at a volumetric flowrate of Q per unit width down a vertical surface obtain from dimensional analysis the form of the relationship between flowrate and film thickness. If the flow is streamline, show that the volumetric flow rate is directly proportional to the density of the liquid. Solution The flowrate, Q, will be a function of the fluid density, ρ, and viscosity, μ, the film thickness, d, and the acceleration due to gravity, g, Or Q = f(ρ,g,μ,d), or : Q = ρagbμcdd where K is constant. The dimensions of each variable are :Q=L2/T, ρ=M/L3,g = L/T2, µ = M/LT and d = L. Equating dimensions: M : 0 = a + c L : 2 = -3a + b – c + d T : -1 = -2b-c From which, c =1 - 2b ,a = -c = 2b - 1, and d = 2 + 3a – b – c = 2 + 6b – 3 – b + 1 - 2b = 3b

12. Q = K(ρ2b-1gbμ1-2bd3b) Qρ/ μ=K(ρ2gd3/ μ 2)b and Q μ1-2b For streamline flow , Q μ1-2b and : -1=1 - 2b and b=1 Qρ/µ=K(ρ2gd3/μ2), Q=K(ρgd3/μ) And: Q is directly proportional to the density, ρ Problem 2 • The power required by an agitator in a tank is a function of the following for variables: • Diameter of impeller • Number of rotation of the impeller per unit time, • Viscosity of liquid, • Density of liquid. • From a dimensional analysis, obtain a relation between the power and the four variables. • The power consumption is found, experimentally, to be proportional to the square of the speed of rotation. By what factor would the power be expected to increase if the impeller diameter were doubled?

13. Solution 2 If the power P=ф(DNρµ), then a typical form of the function is P=kDaNbρcµd, where k is a constant. The dimension of each parameter in terms of M,L, and T are:power, P=ML2/T3, density, ρ =M/L3, diameter, D=L, viscosity, µ = M/LT, and speed off rotation, N=T-1 Equating dimensions: M : 1 = c + d L : 2 = a - 3c - d T : -3 = - b – d Solving in terms of d : a = (5 - 2d) ,b = (3 - d), c = (1 - d) Or : That is :

14. Thus the power number is a function of the Reynolds number to the power m. In fact Np is also a function of the Froude number, DN2/g. The previous may be written as : P/D5N3ρ=K(D2Nρ/µ)m Experimentally : P∞N2 From equation, P∞NmN3, that is m + 3 = 2 and m = -1 Thus for the same fluid, that is the same viscosity and density : (P2/P1)(D51N31/D52N32)=(D21N1/ D22N2)-1 or : (P2/P1) = (N22D32)/(N21D31) In this case, N1=N2 and D2=2D1. D(P2/P1)=8D31/D31=8 A similar solution may be obtained using the Recurring Set method as follows: P=ф(D, N, ρ, µ),f(P, D, N, ρ, µ)=0 Using M, L and T as funtamentals, there are five variables and theree fundamentals and therefore by Buckingham’s theoren, there will be two dimensionaless groups. Choosing D, N, and ρ as the recurring set, dimensionally: D ≡ LL ≡D N ≡T-1 Thus : T ≡N-1 Ρ ≡ML-3M ≡ρL3=ρD3

15. First group, 1, is P(ML2T-3) ≡ P(ρD3D2N3)-1 ≡ P/ρD5N3 Second Group 2, is μ(ML-1T -1) ≡ μ(ρD3D-1N)-1 ≡ μ /ρd2N Thus : Although there is little to be gained by using this method for simple problem, there is considerable advantage when a large number of groups is involved.

16. Problem 3 Obtain by dimensional analysis a function relationship for the wall heat transfer coefficient for a fluid flowing through a straight pipe of circular cross-section. Assume that the effect of natural convection may be neglected in comparison with those of forced convection. if is found by experiment that, when the flow is turbulent, increasing the flowrate by a factor of 2 always results in a 50% increase in the coefficient. How would a 50% increase in density of the fluid be expected to affect the coefficient, all other variables remaining constant?

17. Problem 4 Liquid flows under steady-state conditions along an open channel of fixed inclination to the horizontal. On what factor will the depth of liquid in the channel depend? obtain a relationship between the variables using dimensional analysis. Problem 5 Upon what variables would the rate of filtration of suspension of fine solid particles be expected to depend? consider the flow through unit area of filter medium and express the variables in the form of dimensionless groups. if id found that the filtration rate is doubled if the pressure difference is doubled. What would be the effect of raising the temperature of filtration from 293 to 331 K?