Outflow from orifice

Outflow from orifice

TYPES OF OUTFLOW Outflow steady: z = const, h E = const (H = const, H E = const) Q p = Q quasi-steady: z ~ const., phenomenon of large reseroir unsteady: z const (H const) Q p Q, filling and drawdown of tank (reseroir) Outflow free (a) free outlet jet submerged (b) submerged outlet jet partly submerged, e.g. outflow from large orifices at the bottom (slide gate) K141 HYAE Outflow from orifice 1

STEADY OUTFLOW FROM ORIFICE STEADY FREE OUTFLOW (SFO) OF IDEAL LIQUID p a (=0) BE surface outlet: i h E = p 0 i g h+ + = g g g oerpressure i = ghe Torricelli (1608-1647) equation for outflow elocity of ideal liquid i S orifice for large reseroirs with free leel: section 0 p 0, 0, he h i = gh g u i, i,dq i,q i outflow discharge of ideal liquid Q i : Q = dq = u ds for small orifice (bottom and wall): Q = i i ds Q = S=S i i S i i i S S gh K141 HYAE Outflow from orifice u i i h depth of cente of orifice

CONTRACTION OF OUTLET JET Strip area S c < S, S c = S, contraction coefficient 1 TAB. sharp edged orifice well mouthed orifice partial contraction imperfect contraction re-entrant streamlined mouthpiece external mouthpiece D Hydraulic losses outlet loss Z= c g... depends on shape, setup and size of orifice (structure), Re K141 HYAE Outflow from orifice 3

SFO OF REAL LIQUID FROM ORIFICE AT THE BOTTOM OF TANK BE 0-1 0 h lc g ps0 g pa g c g c g l c ~ 0,5 D Simplification: free leel p s0 = p a S 0 >> S 0 ~ 0 l c << h E l c ~ 0 c p s0 1 1 p g gh l 0 g ps0 g p a g K141 HYAE Outflow from orifice 4 a c... elocity coefficient Q = c S c, S c = εs, εφ = μ orifice discharge coefficient contraction coefficient φ, μ, ε... TAB. 0 c Q S gh, gh

SFO OF REAL LIQUID FROM ORIFICE IN VERTICAL WALL OF TANK - Large orifice h T < ( - 3) a change of outflow elocity u with height of orifice u= gh E Q= 1/ g h ds S E - Open reseroir and large rectangular orifice in ertical wall: ds=b dh E S=ba h E 1/ Q= Q= b g he dhe 3 b g h -h he1 for large tank: 0 h h E g Q= 3 b g h -h 3/ 3/ E E1 3/ 3/ 1 - Small orifice h T > ( - 3)a for S 0 >> S 0 ~ 0 c Q S gh t, gh t K141 HYAE Outflow from orifice 5

Coefficients for discharge determination - small sharp-edged orifice with full contraction 0,97 0,63 0,61 - external cylindrical mouthpiece L/D = 4 0,81 1,00 0,81 - streamlined mouthpiece jet tube 0,95 1,00 0,95 - large orifices at the bottom with significant 0,65 to 0,85 or continuous side contraction - outlet tube of diameter D and length L with free outflow K141 HYAE Outflow from orifice 6 = 1 L 1+ + D φ, ε, μ for imperfect and partial contraction > φ, ε, μ for full contraction empirical formulas Note: special application of outflow through mouthpiece - - Mariotte essel - with function of dilution dosing, Q = const. i

OUTFLOW FROM SUBMERGED ORIFICE for both small and large orifices of whateer shape u gh 0 for small orifice for large reseroir H = H 0 Q μ Q μ S S gh 0 gh Note: solution for partial submergence: Q = Q 1 + Q (Q 1 outflow from free part of orifice, Q outflow from submerged part of orifice). K141 HYAE Outflow from orifice 7

OUTFLOW JETS Free outflow jet connected part Supported outflow jet theoretical trajectory (parabola ) type: water - air decay of jet, aeration, drops Submerged outflow jet type: water air solid surface pulsating margin of boundary layer (mixing regions) jet core with constant elocity type: water - water different functions of jet requirements for outlet equipment and outlet elocity - free jets cutting, drilling, hydro-mechanization (unlinking), firefighting, irrigation jets - submerged jets - dosing, mixing, rectifying, K141 HYAE Outflow from orifice 8

0 sinδ Theoretical shape of outflow jet (projection at an angle) arcing distance of jet x t cosδ y 0 0 t sinδ 1 0 gt δ 0 cosδ 0 L p0 = sin =hd sin g maximum height 0 0 d y = sin =h sin g 0 =hd g energetic head of jet h d For = 45 L p0max = 0 /g = h d, y 0 = 0,5 h d For = X, = 90 -X same arcing distance For = 90 ertical jet y 0max = 0 /g = h d x = t y = 0 1 gt For = 0 horizontal jet (horizontal projection) theoretical L p = h d yt real liquid, large reseroir L = h y p T T K141 HYAE Outflow from orifice 9

UNSTEADY OUTFLOW FROM ORIFICE Q p < Q 0 drawdown, Q p > Q 0 filling Differential equation of unsteady flow Q dt -Q dt =-S dh 0 p 0 Q dt -Q dt =S dh (filling: t 1 t, h 1 h ) p 0 0 S0dh S0dh dt =- = Q -Q Q -Q 0 p p 0 h h h 0 0 1 S dh 1 S dh t =t- t 1= = Q -Q Q -Q 0 p h p 0 (drawdown) the same equation for drawdown and filling For Q p const., S 0 const., irregular reseroir numerical solution in interals t K141 HYAE Outflow from orifice 10

Drawdown of prismatic tank (S 0 = const.), at Q p = 0 Assumptions: - outflow from small orifice, mouthpiece, tube - free leel - S 0 >>S 0 ~ 0 Q = 0 S gh S0 t = h dh S g h1-1/ S0 t = h 1- h h S g Time of total emptying (h = 0): S h S h V T = = = S g S gh Q 0 1 0 1 1 1 01 K141 HYAE Outflow from orifice 11