## DV Sentence Examples

- For by (30) do =
**dv**, and by (2)**dv**is proportional to ds. - ,In a fluid, the circulation round an elementary area dxdy is equal to
**dv**du udx + (v+dx) dy- (u+dy) dx-vdy= () dxdy, so that the component spin is**dv**du (5) 2 dx - dy) in the previous notation of § 24; so also for the other two components and n. - The heat absorbed in isothermal expansion from vo to v at a temperature 0 is equal to the work done by equation (8) (since d0 =o, and 0(dp/d0)
**dv**=pdv), and both are given by the expression RO log e (v/vo). - Since by definition E_ - v(dp/
**dv**) =p(dp/dp) equation (6) becomes U = (dp / dp) (7) The value U = / (E/p) was first virtually obtained by Newton (Principia, bk. - Linke's mean value for
**dV**/dh at the ground was 125. **Dv**, Velar area or cephalic dome.- If we denote the critical volume, pressure and temperature by Vk, Pk and Tk, then it may be shown, either by considering the characteristic equation as a perfect cube in v or by using the relations that dp/
**dv**=o, d 2 p/**dv**2 =o at the critical point, that Vk = 3b, Pk= a/27b2, T ic = 8a/27b. **Dv**, vessel.**Dv**, dorsal vessel passing into central sinus (bs).- Tsm l, Tergo-sternal muscle (labelled
**dv**in fig. **Dv**' to**dv**s, Dorso-ventral muscles (same as the series labelled tsm in fig.**Dv**' to**dv**s, Dorso-ventral muscles (same as the series labelled tsm in fig.- Tsm, Tergo-sternal muscles, six pairs as in Scorpio (labelled
**dv**in fig. - (1), the effect at B is l abX 2 a+b - cos 2 T t f cos 27rv 2 .
**dv**+sin 27t f sin27rv .**dv**(3), the limits of integration depending upon the disposition of the diffracting edges. - The intensity I 2, the quantity with which we are principally concerned, may thus (be expressed I 2 = 3 fcos27rv 2 .
**dv**} 2 2 t 2 These integrals, taken from v =o, are (known as Fresnel's integrals; we will denote them by C and S, so that C = fo cos 27rv 2 .**dv**, S = fjsinv 2 .**dv**. - From the series for G and H just obtained it is easy to verify that dH = - 7rvG,
**dv**av - dG _ 7rvH -1. - (19), 1 abA) ' ' we may write 12= (cos 27rv 2 .
**dv**) 2 + (f sin zirv 2 .**dv**) 2 (20), or, according to our previous notation, 12 = (2 - C 2 +(z - Sv)2= G2 +H2 Now in the integrals represented by G and H every element diminishes as V increases from zero. - 19, where, according to the definition (5) of C, S, x =i v cos 27rv 2 .
**dv**, y = f v sin ?7rv 2 .**dv**.. - For dx=cos airv 2 .
**dv**, dy= sin 271-v2.**dv**; so that s = f (dx 2 +dy 2) =v, (30), 0= tan1 (dyldx) =171-v 2 (31). - Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP
**dV**(5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential. - Dp dpu dpv dpw -z)' reducing to the first line, the second line vanishing in consequence of the equation of continuity; and so the equation of motion may be written in the more usual form du du du du d dt +udx+vdy +wdz =X -n dx' with the two others
**dv****dv****dv****dv**i dp dt +u dx +v dy +w dz - Y -P d y' dw dw dw Z w dw i d p dt +u dx +v dy +wd - -P dz. - (5) (8) (I) The components of acceleration of a particle of fluid are consequently Du dudu du du dt = dt +u dx +v dy + wdz' Dr
**dv****dv****dv****dv**dt -dt+udx+vdy+wdz' dt v = dtJ+udx+vdy +w dx' leading to the equations of motion above. - Eliminating H between (5) and (6) DS du
**dv**dw (du**dv**d1zv dt u dx n dx udx' 5 -, dzi =°' and combining this with the equation of continuity Dp du**dv**dw p iit dx+dy+ dz = °' (10) D i du n**dv**dw_ dt (p p dx p dx p dx - o, with two similar equations. - Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/
**dv**=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which**dv**is drawn perpendicular. - If r denotes the radius of curvature of the stream line, so that I dp +
**dV**- dH _ dq 2 q2 (6) p**dv****dv****dv****dv**- r ' the normal acceleration. - If r denotes the radius of curvature of the stream line, so that I dp +
**dV**- dH _ dq 2 q2 (6) p**dv****dv****dv****dv**- r ' the normal acceleration. - - In the uniplanar motion of a homogeneous liquid the equation of continuity reduces to du
**dv**dx' dy-O' u= -d,y/dy, v = d i t/dx, (2) surface containing so that we can put _ (6) (9) we have (I) (2) (5) (I) where 4 is a function of x, y, called the streamor current-function; interpreted physically, 4-4c, the difference of the value of 4, at a fixed point A and a variable point P is the flow, in ft. - 1 = yv24, (2) y 2 y y y suppose; and in steady motion, + y 2 dx v-t ' = o, dH +y 2dy0 2P = o, so that 2 "/ y = - y2, 7 2 1,G = dH/d is a function of 1,G, say f'(> '), and constant along a stream line; dH/
**dv**= 2qi', H -f (1/.) = constant, throughout the liquid. - The kinetic energy of the liquid inside a surface S due to the velocity function 4' f i (s given by T=2p + (d) 2+ (t) dxdydz, pff f 75 4 dS (I) by Green's transformation,
**dv**denoting an elementary step along the normal to the exterior of the surface; so that d4ldv = o over the surface makes T = o, and then (d4 2 d4) 2 'x) + (dy) + (= O, dd? - Again, since d4)/
**dv**=d /ds, d4)/ds= - d4y/**dv**, (13) T = 1 p f(1 9 d = - 2 p f4' d (14) With the Stokes' function, y for motion symmetrical about an axis. - ZI /t = - (a - s) M'Q 2 sine cos ° - EQ sin() =[ - (a - (3)M'U+E]V (8) Now suppose the cylinder is free; the additional forces acting on the body are the components of kinetic reaction of the liquid - aM' (Ç_vR), - (3M' (-- E -FUR), - EC' dR, (9) so that its equations of motion are M (Ç - vR) _ - aM' (_vR) - (a - $) M'VR, (io) M (Ç+uR) = - OM' (
**dV**+U R) - (a - ()M'UR - R, '(II) C dR = dR + (a - Q)M'UV+0V; (12) and putting as before M+aM'=ci, M+13M' = c2, C+EC'=C3, ci dU - c2VR=o,**dV**+(c1U+E)R=o, c 3 dR - (c 1 U+ - c 2 U)V =o; showing the modification of the equations of plane motion, due to the component E of the circulation. **Dv**, The ductus venosus.- The calculation can be carried out in each region of velocity from the formulae: (25) T(V) - T(v) =k f vvm
**dv**, S(V)-S(v) =k f vvm+ldv I (V)-I(v)=gk v vv m-ldv, and the corresponding integration. - For the simplest case of polarized waves travelling parallel to the axis of x, with the magnetic oscillation y along z and the electric oscillation Q along y, all the quantities are functions of x and t alone; the total current is along y and given with respect to our moving axes by __ (d_ d Q+vy d K-1 Q, dt dx) 47rc 2 + dt (4?rc 2) ' also the circuital relations here reduce to _ dydQ _dy _ dx 47rv ' _ dt ' d 2 Q
**dv**dx 2 -417t giving, on substitution for v, d 2 Q d 2 Q d2Q (c2-v2)(7372 = K dt 2 2u dxdt ' For a simple wave-train, Q varies as sin m(x-Vt), leading on substitution to the velocity of propagation V relative to the moving material, by means of the equation KV 2 + 2 uV = c 2 v2; this gives, to the first order of v/c, V = c/K i - v/K, which is in accordance with Fresnel's law. - In the notation of the calculus the relations become - dH/dp (0 const) = odv /do (p const) (4) dH/
**dv**(0 const) =odp/do (v const) The negative sign is prefixed to dH/dp because absorption of heat +dH corresponds to diminution of pressure - dp. The utility of these relations results from the circumstance that the pressure and expansion co efficients are familiar and easily measured, whereas the latent heat of expansion is difficult to determine. - It is often impossible to observe the pressure-coefficient dp/de directly, but it may be deduced from the isothermal compressibility by means of the geometrically obvious relation, BE = (BEÃ†C) XEC. The ratio BEÃ†C of the diminution of pressure to the increase of volume at constant temperature, or - dp/
**dv**, is readily observed. - We thus obtain the expressions dH = sdo +0 (dp I dO)
**dv**= Sd0 - o (**dv**/do) dp.. - If we put dH=o in equations (8), we obtain the relations between
**dv**and do, or dp and do, under the condition of no heat-supply, i.e. - The change of energy at constant volume is simply sdo, the change at constant temperature is (odp/de - p)
**dv**, which may be written dE/de (v const) =s, dE/**dv**(0 const) =odp/do - p . - We thus obtain the relation ds/
**dv**(o const) =od 2 p/d0 2 (v const),. - The equation to these lines in terms of v and 0 is obtained by integrating dE=sd0+(Odp/de - p)
**dv**= o . - The isothermal elasticity - v(dp/
**dv**) is equal to the pressure p. The adiabatic elasticity is equal to y p, where -y is the ratio S/s of the specific heats.