# Dp Sentence Examples

Recalling the formulae above which connect s P4 and a m, we see that dP4 and

**Dp**q are in co-relation with these quantities respectively, and may be said to be operations which correspond to the partitions (pq), (10 P 01 4) respectively.But by Green's transformation f flpdS = f f PPdxdydz, (2) thus leading to the differential relation at every point = dy

**dp**The three equations of equilibrium obtained by taking moments round the axes are then found to be satisfied identically.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.From the gas-equation in general, in the atmosphere n d

**dp**_ I**dp**1 de _ d0 de i de (8) z p dz-edz-p-edz-k-edz' which is positive, and the density p diminishes with the ascent, provided the temperature-gradient de/dz does not exceed elk.With uniform temperature, taking h constant in the gas-equation,

**dp**/ dz= =p / k, p=poet/ k, (9) so that in ascending in the atmosphere of thermal equilibrium the pressure and density diminish at compound discount, and for pressures p 1 and 1, 2 at heights z 1 and z2 (z1-z2)11?Thus if T is expressed as a quadratic function of U, V, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi

**dp**' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..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.Substituting for H its value from (3), and employing the notation of the calculus, we obtain the relation S - s =0 (

**dp**/do) (dv/do),.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.AdvertisementSince dE=dH - pdv, we have evidently for the variation of the total heat from the second expression (8), dF=d(E + pv) =dH+vdp=Sde - (Odv/de - v)

**dp**.Thus after a time dt the values of the coordinates and momenta of the small group of systems under consideration will lie within a range such that pi is between pi +pidt and pi +

**dp**,+(pi+ap?dpi) dt „ qi +gidt „ qi+dqi+ (qi +agLdgi) dt, Thus the extension of the range after the interval dt is**dp**i (i +aidt) dq i (I +?gidt).The difference in the lowering of vapour pressures

**dp**-**dp**' may be put equal to VdP/v, where P is the osmotic pressure, and V the specific volume of the solvent.If

**dp**is the difference of vapourpressure of solvent and solution, and do the rise in the boiling-point, we have the approximate relation, n/N = d p/p = mLdo/Ro 2, Raoult's law,..Draw any line DE perpendicular to AB and meeting the circle in E, and take a point P on DE such that the line

**DP**=arc BE; then the locus of P is the companion to the cycloid.AdvertisementThe

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