Water is flowing at a rate of 15 km/hr through a cylindrical pipe of radius 7cm into a rectangular tank which is 50m long and44m wide. In how many hours will the water level in the tank raise by 21 cm?
speed=15km/hR(15*1000)/3600=4.167m/s, h of pipe=f(t),where f(t)=4.167t,to solve,vol of pipe=voL of tank,
LBH=22/7*R"2*4.167T(h) . From here t= LBH/(Pi*r*4.167) t= 50*44*0.21(in m)/(pi* (0.07)"2*4.167)=7202.3 seconds
(15 km/hr * 10^5 cm/km) * (49π cm^2) * x hr = (50m * 44m)(100cm/m)^2 * 21cm
x = 2 hr
To answer this question, we need to determine the volume of water flowing into the tank per unit of time. Then, we can calculate the time it takes for the water level to raise by 21 cm.
First, let's calculate the area of the cylindrical pipe:
Area = π * radius^2
Radius = 7 cm = 0.07 m
Area = 3.14 * (0.07)^2 = 0.1539 m^2
Next, we need to find the volume of water flowing into the tank per hour:
Volume = Area * Speed
Speed = 15 km/hr = 15000 m/hr (since 1 km = 1000 m)
Volume = 0.1539 m^2 * 15000 m/hr = 2308.5 m^3/hr
Now, let's calculate the volume of water required to raise the water level in the tank by 21 cm:
Volume_needed = Length * Width * Height
Length = 50 m
Width = 44 m
Height = 0.21 m (convert 21 cm to meters)
Volume_needed = 50 m * 44 m * 0.21 m = 462 m^3
Finally, we can determine the time it takes for the water level to raise by 21 cm:
Time = Volume_needed / Volume
Time = 462 m^3 / 2308.5 m^3/hr ≈ 0.2 hr
Therefore, it will take approximately 0.2 hours (or 12 minutes) for the water level in the tank to raise by 21 cm.