By Ludwig Prandtl, O. G. Tietjens, Engineering

Prandtl's pioneering experiments laid the root for using theoretical hydromechanics and hydrodynamics in sensible engineering difficulties. This quantity offers Tietjens' recognized growth of Prandtl's lectures: statics and kinematics of beverages and gases, dynamics of non-viscous drinks. Proofs use vector analysis.

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Extra resources for Fundamentals of Hydro- and Aeromechanics

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Surface warming, as a result of which an unstable distribution is produced. ) continually stirred up. The thermal expansion of the lower air layers lifts the upper layers somewhat. This displacement has not been shown in Fig. 26 for the sake of simplicity. , mists or clouds are formed; and thereafter the distribution curve is a saturated adiabatic. With uniform humidity and uniform initial temperature, condensation takes place simultaneously for all the parallel air currents and the 44 FUNDAMENTALS OF HYJ)RO- AND AEROMECHANICS clouds have a horizontal bottom appearing to be floating on a horizontal mass of air (Fig.

H t he exception . f change of density. water wit 0 two communicating vessels; the remaining liquid must then be in equilibrium in this form. A practical application of such communicating tubes is found in liquid manometers which are frequently used in measuring pressures. If the manometer shown diagrammatically in Fig. p'o 8a has a gas enclosed in its right stem and a water column of height h in the left stem, then -1 + vb, + "(h Pl = po Pl = P h f 2, so that P = Po + "((hl - h 2 ) = P» + "(h, or P, b FIG.

Eliminating v by the equation of state pv = BT, we obtain p( BpT ) n = const. or ~BT pn - or T = If T = T I when p = const. - -7J-P n • then = PI, n-l T= T{;)-n (8) Introducing the expression for T given by (2), we get n-l (PI h2 - h-i 1 = BTIPI --n-Jp2 p - ndp or or h 2- hI = _n hall _ (p2)n~I(. n - 1 PI \ (9) This formula gives the relation between pressure and height. An analogous connection between temperature and height can be obtained by introducing n-l (~:)-n- = ~: into Eq. (9). »: h _ T2) n - 1 o(l T I or (10) APPLICATION OF THE PRESSURE EQUATION 33 stating that in a polytropic atmosphere the temperature is a linear function of the height.

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