Temperature 7477

The pool with a length of l = 50 m and a width of s = 15 m has a depth of h1 = 1.2 m at the shallowest part of the wall. The depth then gradually increases to a depth of h2 = 1.5 m in the middle of the pool. = 4.5 m walls in the deepest part of the pool. Consider the specific heat capacity of water c = 4,200 J / (kg · °C).

a) What is the volume of water in the pool?
b) How long does it take to fill the pool with two inlets if each flows A = 5 liters / s?
c) How much GJ of heat is needed to heat the pool water by ∆t = 10 °C?
d) When filling the pool for the first time, we require that the water has a temperature of t = 25 °C.
How much hot water and how much cold water will we need if the temperature of cold water t1 = 10 °C and hot water t2 = 60 °C?

Correct answer:

V =  1631.25 m3
t =  45.3125 h
E =  68.5125 GJ
a =  1141.875 m3
b =  489.375 m3

Step-by-step explanation:

l=50 m s=15 m h1=1.2 m h2=1.5 m h3=4.5 m c=4200 J/kg/°C  S1=(h1+h2)/2 2l=(1.2+1.5)/2 250=4135=33.75 m2 S2=(h2+h3)/2 2l=(1.5+4.5)/2 250=75 m2  V=s (S1+S2)=15 (4135+75)=46525 m3=1631.25 m3
V1=V l=V 1000  l=1631.25 1000  l=1631250 l Q=5 l/s t1=V1/(2 Q)=1631250/(2 5)=163125 s t=t1 h=t1:3600  h=163125:3600  h=45.313 h=16725 h=45.3125 h
h=1000 kg/m3 m=h V=1000 46525=41000 6525=46525000=1631250 kg T=10 °C E1=m c T=1631250 4200 10=68512500000 J E=E1/109=68512500000/109=805481 GJ=68.5125 GJ
a+b = V 10a + 60b = 25V  a+b=1631.25 10a+60b=25 1631.25  a+b=1631.25 10 a+60 b=25 1631.25  a+b=1631.25 10a+60b=40781.25  Pivot:Row1Row2 10a+60b=40781.25 a+b=1631.25  Row2101 Row1Row2 10a+60b=40781.25 5b=2446.88  b=52446.875=489.375 a=1040781.2560b=1040781.2560 489.375=1141.875=89135 m3=1141.875 m3  a=89135=1141.875 b=83915=489.375
b=489.375=83915 m3=489.375 m3

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