Question

L 2. Steady statemass balance: Water is flowing at steady state in a 0.1 meter-diameter pipe with a maximum velocity (turbulent profile) of 0.3 meters/sec. The pipe then goes through an expansion, to where it is then flowing in a 0.5 meter-diameter pipe, and the flow regime has changed from turbulent to laminar. In the second section of pipe, calculate the velocity as (a) block flow profile (Vavg), and (b) maximum velocity in laminar flow profile? HINT: you will need to use the velocity relationships in Table 3.1 from the text (slide 14 in Chap 3 Powerpoint). L 3. Steady state mass balance: An above-ground water supply tank (tower) has an inflow pipe of 2-ft diameter, and two outflow pipes, one that is 1-ft diameter and the other that is 0.5 ft-diameter. The constant velocity in the inflow pipe is 3 ft/sec. The velocity out of the 0.5 ft pipe is 7 ft/sec. The water level in the tank is not changing (steady state). What are the mass flow rate and the velocity of the outflow out the 1.0 ft discharge pipe? Draw a schematic of this system and show your control volume. Unsteady state mass balance: An oil product tank (upright circular cylinder) of diameter 50 ft and height of 20 ft has an open top. A constant flow of gasoline is pouring into the tank at 1,100 gals/minute 4. (gpm), while a constant outflow from near the tank bottom is occurring at 600 gpm. At the time both of these flows started, the tank was 80 % full. What amount of time (hours/minutes) will elapse from the time these flows started until the tank overflows? 1. Steady state mass balance: At point A, the water flowing in an open storm drain has a cross-sectional area of 300 ft. At this location in the drainage system, the average flow velocity is 3 ft per second. At point B, mile downstream, the drainage cross-section is a rectangle of dimensions 50 ft wide by 12 ft deep. Between point A and point B, there is a drain pipe from a large parking lot that discharges into the main storm drain system with a constant flow of 80 cubic feet per second (cfs). If all flows are steady state, what is the total flow rate at point B in cfs? Also, what is the average velocity of the water flow at point B? Perform and show all your calculations in English units, namely velocity in ft per second, area in square feet, and volumetric flow rate in cfs. You must also include a diagram that shows your control volume for this problem (suggest the CV be a plan view map of the storm drain system). 2. Steady state mass balance: Water is flowing at steady state in a 0.1 meter-diameter pipe with a maximum velocity (turbulent profile) of 0.3 meters/sec. The pipe then goes through an expansion, to where it is then flowing in a 0.5 meter-diameter pipe, and the flow regime has changed from turbulent to laminar. In the second section of pipe, calculate the velocity as (a) block flow profile (Vavg), and (b) maximum velocity in laminar flow profile? HINT: you will need to use the velocity relationships in Table 3.1 from the text (slide 14 in Chap 3 Powerpoint). 3. Steady state mass balance: An above-ground water supply tank (tower) has an inflow pipe of 2-ft diameter, and two outflow pipes, one that is 1-ft diameter and the other that is 0.5 ft-diameter. The constant velocity in the inflow pipe is 3 ft/sec. The velocity out of the 0.5 ft pipe is 7 ft/sec. The water level in the tank is not changing (steady state). What are the mass flow rate and the velocity of the outflow out the 1.0 ft discharge pipe? Draw a schematic of this system and show your control volume. 4. Unsteady state mass balance: An oil product tank (upright circular cylinder) of diameter 50 ft and height of 20 ft has an open top. A constant flow of gasoline is pouring into the tank at 1,100 gals/minute (gpm),while a constant outflow from near the tank bottom is occurring at 600 gpm. At the time both of these flows started, the tank was 80% full. What amount of time (hours/minutes) will elapse from the time these flows started until the tank overflows? Flow Distributions TABLE 3.1 Comparisons of block flow, turbulent and laminar velocity distributions Laminar low Turbulent flow Block flow 2.00 Vverge 1.22 Vaverage Vaverage Vaverage Vaverage Maximum velocity Minimum velocity average average 2.00 1.06 2 2 Kinetic energy per unit mass 2 1.333-Vaverage PA 1014 Vverage pA Vverage PA Total momentun in the Bow

Answer 1

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3)
2 di2 4,3 ft d30Pt 7ftls As velocty fs censtant thragheut the pipe meane its avevge veloeity valuc So ,u, U3 are flew in So A u ayaudag. 2 flow Cut A3 4 2 2 T 4 4 4 /2 Formula for mass flew rati m AUavStho So mC2-43 x ndix Uaug,ay default flutd - 62-43-bn 4 62.43mx 3-14 x 2t)x 3(ft) 62.43 x 3-14 x 3 bm 588-38 bm Bee Ans Smilarly m2 62.43x 314x2 X IO.25 4 502 5a bm/sec Ary 2 CS Scannedgh62-43 x 3-14 x CamScanner
Mass flow rate will always be conserve as 502.581+85.06= 588.38 which is inflow mass rate shows our calculation is correct.