8-99 M,Y and O. E:\public_html\8-99 elevated tank problem.mcd 1 / 11 9/4/99 / 8:03 AM elevated tank problem.mcd last save 9/4/99 / 8:03 AM

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1 8-99 M,Y and O The pressure at section shown in the Fi. below is not to fall below 50 lb / in when the flowrate in the tank varies from 0 to cfs and the branch line is shut off. Determine the minimum heiht h of the water tank under the assumption that (a) minor losses are neliible; (b) minor losses not neliible last save E:\public_html\ /

2 known data: psia :=.7 psi k density of water r := 999 vapor pressure of water p m 3 v :=.5 psia viscosity of water m :=.00 newton sec ft of water =.33 psi m unit weiht of water 6. lbf := ft 3 p d pipe diameter d := 6 in area of pipe A 6 := ft 3 ft 3 ft 3 :=.,.5.. rane of flows used sec sec sec Use the "Blasius equation" for smooth pipes, that is pipes with a Reynolds number of less than 00,000. In such a situation the friction factor, f, is function of the Reynolds number, f = f(re). flow velocity as a function of : ( ) := A 6 Reynolds number as a function of : Re( ) := r d ( ) m velocity at water surface in elevated tank : V s := 0 ft sec last save E:\public_html\ /

3 f( ).36 := : Blasius Equation for "smooth pipes", Re < 0 Re( ) elevation at the dischare tap z ( 0 ft + h ft + 6 ft) 5 elevation at the water surface in the tank z s := 0 ft pressure at the water surface in the tank := 0 psi p := 50 psi - residual pressure at the "tap" lenth of pipe in the system L h ft ft ft + 6 ft h ft V s + z s + f L d p + z + + z s + V s f ( h ft) d p 6 ft h + Has solution(s) which are the heads required for a variety of flow rates in order to maintain a dischare pressure of 50 psi. last save E:\public_html\ 3 /

4 h, p := V s + z s f( ) d f( ) d ( ) ( ) + p ft + 6 ft ( ) 00 Head required for flow at 50 psi heiht of tank (ft) h[, 50( psi ) ] ft h[, 60( psi ) ] ft ft 3 sec flowrate residual pressure = 50 psi residual pressure = 60 psi Note the tradeoff, for a specified flow a hiher residual pressure desired at the tap requires a hiher tank last save E:\public_html\ /

5 Now consider what happens if the amount of head available is fixed, as in the case of an existin elevated tank. The curves indicate that hiher demands require hiher pressures. For a specific system with a fixed amount of head an increase in demand means a drop in pressure. Now Include Minor Losses minor loss coefficient K L :=.3 pressure at the tap: p = 50psi Bernoulli's Equation + z s + V s f ( h ft) D 5 K L p 6 ft h + solve it for the heiht of the elevated tank h t ( ) := V s + z s f( ) d ( ) 5 ft f( ) d K L ( ) + ( ) p + 6 ft ( ) last save E:\public_html\ 5 /

6 00 heiht vs flowrate, includes minor loss heiht of tank, ft. h t ( ) h[, 50( psi ) ] ft Flowrate (cfs) heiht with minor losses included, 50 psi heiht w/o minor losses, 50 psi Minor losses make more difference at hiher flowrates last save E:\public_html\ 6 /

7 Now consider the case of a specific elevated tank with a fixed heiht. Solvin Bernoulli's equation for the pressure at the dischare for a fixed tank heiht we et: h := 00 ft : fixed tank heiht al al := 50, min min al min + z s + V s f ( h ft) d A 6 p 6 ft h + A 6 p ( ) := d A 6 z s d A 6 V s d A 6 + f( ) h 506 f( ) + ft 3 ft d A 6 h d A 6 p ( ) psi Pressure at tap vs Demand pressure at the tap, psi al min last save E:\public_html\ 7 /

8 As the demand ets reater the pressure at the tap drops. What, if anythin, does it mean when the pressure becomes neative Now Look at the Branch Line Look at the drawin aain. See the branch line comin off the main dischare? So far the ate valve to that line has been closed. Inorin elevation differences the branch line runs to a lare tank on a farm, as shown below: vent (screened) storae tank branch line off main line lenth of pipe from main line to water surface = 00' depth in tank (variable) last save E:\public_html\ 8 /

9 Suppose that durin a period of hih demand the ate valve is opened to add water to an insecticide solution already in the tank. This solution will then be withdrawn by a tractor with a sprayin attachment for crop application. What are the possibilities. How many of them are ood? lenth of pipe up to the ate valve L h ft ft + 6 ft h ft where h = 00' al al := 50, min min al min p ate ( ) := d A 6 z s d A 6 V s d A 6 + f( ) h 706 f( ) + ft 3 ft d A 6 h d A 6 d A 6 + d p ate ( ) psi Pressure at ate valve to branch line The Bi uestion - What happens to the liquid in the tank when the valve is opened al min last save E:\public_html\ 9 /

10 ft_ho :=.33 psi.7 psi = 57.0ft_HO last save E:\public_html\ 0 /

11 d A 6 + d last save E:\public_html\ /