introduction to fluid mechanics

... beginning of fluid mechanics Fig 1.3 Ancient Greek ship depicted on old vase inclination or supply pressure had to be adjusted to overcome friction with the wall of the conduit This gave rise to much ... was the first to find the least resistive ‘streamline’ shape 4 History of fluid mechanics Leonardo da Vinci (145 2-1 519 ) An all-round genius born in Italy His unceasing z...

Ngày tải lên: 22/10/2012, 10:59

... Kinematic viscosity B Y units 0 1 0 0 m kg -3 -1 1 1 -1 -1 -2 -2 -2 -2 -1 -1 S mls m/s2 kg I m3 N = kg m/s2 Pa = N/m2 J Pa s m2/s Characteristics of a fluid 2.2.2 Dimension All physical quantities ... proportional to the velocity gradient duldy Such fluids are called Newtonian fluids On the other hand, liquid which is not subject to Newton's law of viscosit...

Ngày tải lên: 22/10/2012, 10:59

... semiconductor strain gauge PGM-C Pressure range (MPa) Natural frequency (kHz1 Response frequency (kHz1 PE-J, P (a) Small size 0. 2-1 o 2 5-4 0 5-8 (b) For indicating pressure of an engine 5-2 0 2 5-4 0 5-8 ... pdAor ( ) p+-dz dA-pgdAdz=O 24 Fluid statics Fig 3.4 Balance of vertical minute cylinder dp _ - -PS &" (3.6) Since p is constant for liquid, the following equation ens...

Ngày tải lên: 22/10/2012, 10:59

... direction moves to A‘B’ while rotating by dq, and AD in the y direction rotates by de, Thus av de - - dxdt - ax at4 d = dydt E aY de - L = - d av d~ t I - dx ax de = dt dE2 dy au - ay The angular ... case of two-dimensional flow where w = V is an operator which represents a a a ax ay az i-+j-+k- where i,j , k are unit vectors on the x, y z axes 50 Fundamentals of f...

Ngày tải lên: 22/10/2012, 10:59

... momentum: - (D’ increase in momentum: R - d2)pu: 71 -p[D2u: 71 + -d’pui - (0’ - d2)u: - d’ui] 71 force acting on the fluid: -D’(p, - p ) By the law of momentum, ~ [ D ’ u - (D’ - d2)u: - d ’ ~ ... respectively Then from Bernoulli’s equation Pl u: 2g P2 -+ -+ z PS VI - PS 29 +-+ z2 Assuming that the pipe line is horizontal, z1 = 22 v2 - v: -...

Ngày tải lên: 22/10/2012, 10:59

... following equation: a u a u au du = -dt + dx -dy at ax ay + Therefore, du _ - -au + -audx- ~ -audy- + ~ -+ +u dt at axdt aydt at au ax aU ay Substituting this into eqn (6.4), Next, the force F acting ... d y = -h3 dP 12pdx From this equation, the mean velocity u is Q = - = -h2 dP = - u1 h 12pdx 1.5 (6.23) (6.24) The shearing stress z due to viscosity becomes ldp z = p - d...

Ngày tải lên: 22/10/2012, 10:59

... efficiency q for a diffuser is therefore P2-P1 - q=-P2th - PI hs (0: - U:)/2s (7.31) Substituting in eqn (7.28), the above equation becomes q = - c - 02 - - + 02 - Al/A2 + Al/A2 (7.32) Convergent pipe ... losses in pipe lines 125 P P -+ - v: = -+ -+ P9 29 h, 29 P9 Therefore €72 - PI - - P9 hs 29 (7.29) Putting pzth p for the case where there is...

Ngày tải lên: 22/10/2012, 10:59

... (8.6) and (8.7) (-) v =- A 2'3i1,2 n s Q = -1 i A5/3 - ll2 n s2I3 A = r2(;) - ?cos(;) = r2(e- sin e) sin(;) s = re ( m = - 1-2 r si:e> i.e n -T)] Z( 1-7 ) sin 'I3 v=-i112[;(1 Q = -i'121 n sine 'I3 ... cross-sections are uniform and whose banks are covered with wild grass Bending river with large stones and wild grass 0.01 0-0 .013 0.01 2-0 .018 0.01 3-0 .017 0.01...

Ngày tải lên: 22/10/2012, 10:59

... Bernoulli’s equation produces the following result: u2 Pd +P2 +2 pm -= p P-Pm= - -Po, PU2/2 p(U2 - Ui) (1 -4 sin28) - pu’ - -4 sinz0 (9.6) The drag of a body 151 Table 9.2 Drag coefficients for ... Drag and lift L=2 -( p-p,)rodBsin8 1n/2 ( I', u+roo = - r o p u r - 2U sin [I -XI2 (k) sin dB = - r o p U r [l - r w - z4s r n B - s i n io -4 2...

Ngày tải lên: 22/10/2012, 10:59

... = [L-’MT-’][L-3M]“[L T-’]’[L]” - L 1-3 x+y+zMl+xT-l-y (10.5) i.e L: - I - ~ x + Y + z = O M: T: l+x=O -l-y=O Solving the above simultaneously gives x =-1 y =-1 z =-1 Substituting these values into ... the first non-dimensional group n, formed with D, is n1 = DpxUydz= [LMT-2][L-'M3x[LT-']y[L]' - L 1-3 x+y+zMl+xT-2-y ' (10.3) In general the basic dimensions in dynamics...

Ngày tải lên: 22/10/2012, 10:59

... _ -1 tl t2 - Fig 11.14 Ultrasonic flowmeter Q -k UCOS6 t, = a - Ucose a + u c o s e - a - u c o s e - 2ucose 1 Measurementof flow discharge 193 where a is the sonic velocity in the fluid From ... Measurement of flow velocity 183 Fig 11.1 NPL-type Pitot tube Fig 11.2 Cylinder-type Pitot tube Fig 11.3 Five-hole spherical Pitot tube 184 Measurement of flow velocity and f...

Ngày tải lên: 22/10/2012, 10:59

... (12.18) aw aw dw=-dx+-dy= ax ay = (u - iu)dx + (u + iu)dy = (u - iu)(dx + i dy) = (u - iu)dz Therefore dw _ - -1 u -u dz (12.19) Consequently, whenever w(z) is differentiated with respect to z, as shown ... ideal fluid Fig 12.1 Balance of pressures on fluid element viscous term of eqn (6.12) is omitted Consequently the following equations are obtainable: (E ; t) : (E Z...

Ngày tải lên: 22/10/2012, 10:59

... the following equations: & - = c dq T " - -T - = c dp- - ( k -d Tc dR c, l) T p T dP OP Sonic velocity 221 s - s1 = s2 - s1 = c"log[ s2 - s1 T ,( , ;f, "il ] (9k(;)k-1] (13.19) ( 13.20) = culog[y' ... variables in the vessel), eqn (13.37) gives k - -1 T + ~2 R = k k k - RT, or k-ld k-1 M2 (1 3.38) RT T - + -= k lk-1u2 are respectively called the tot...

Ngày tải lên: 22/10/2012, 10:59

... - 2-/ 3 ( 4.13) v Substituting eqns (14.12) and (14.13) into (14.11) gives A d2p2 32vdp2 -+ 7-+ -( p2-p*)=0 dt2 D dt plBV Now, writing 16v c=jjj-G mn=@ P2-p1=P then d2P+ 2cmn- + m;p = dP dt2 dt - ... as the sectional area of the pipe, pgAldu p g A ( H - h, - h2) = -9 dt (14.15) giving v2 h-k =kI - d2g v2 2g h - - v2 - 2g and v2 Edv H-(k+l )-= -( 14....

Ngày tải lên: 22/10/2012, 10:59

... method 253 ii,j =t(C-1.j + li,j-i z[($i+l,j - ($i.j+l ICI = i ( $ i - i , j 1.1 ' + Re + li+l,j - $i-I,j)(li,j+i - +i,,-l)(li+1,j + +i,j-I + + $i+I,j li,j+i) - li,j-1) ( 5.10) - li-l.j)l + $t,j+i ... 15.2 Flow in a sudden expansion 9a* - *,+I,] ax aY - *1,1+1 - 2*8,1 *l,l-, -2 k1 ax2 e Fig 15.3 Grid mesh and grid points - *1, 1-1 2h * 1-1 .] 3ay2...

Ngày tải lên: 22/10/2012, 10:59