Water is flowing at the rate of 5km/hr through a cylindrical pipe of radius 7cm into a rectangular tank which is 50m long and 44m wide. In how many hours will the water level in7 cm of tank to filled
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volume=flowrate*area*time
50*44*.7 m^3=5000m/hr*PI (.7/2)^2 *time
solve for time
time=50*44*.7/(5000*PI*(.7/2)^2) hr
50 hr
To find the time it takes to fill the tank by 7 cm, we need to calculate the volume of water that flows through the pipe per hour, and then determine how many hours it takes to fill the tank by 7 cm.
First, let's calculate the volume of water that flows through the pipe per hour:
The rate of flow is given as 5 km/hr. Since the pipe is cylindrical, we can calculate the flow rate in terms of the volume per hour.
The formula for the volume of a cylinder is V = π * r^2 * h, where V represents the volume, r represents the radius of the cylinder, and h represents the height.
Given:
Radius of the pipe (r) = 7 cm = 0.07 m
Rate of flow (v) = 5 km/hr
To find the volume of water flowing per hour, we first need to calculate the cross-sectional area of the pipe:
Area (A) = π * r^2
= π * (0.07^2)
≈ 0.15394 m^2
Now, we can find the volume of water flowing per hour by multiplying the flow rate by the cross-sectional area:
Volume per hour = v * A
= 5 km/hr * 1000 m/km * 0.15394 m^2
≈ 769.7 m^3/hr
Next, we can calculate how long it takes to fill a 7 cm height in the tank:
The tank has dimensions of length (L) = 50 m and width (W) = 44 m.
The volume of water required to fill a 7 cm height in the tank is given by:
Volume = L * W * h
= 50 m * 44 m * 0.07 m
= 154 m^3
Finally, we can calculate the time it takes to fill the tank by dividing the volume required by the volume of water flowing per hour:
Time = Volume / (Volume per hour)
= 154 m^3 / 769.7 m^3/hr
≈ 0.2 hours or 12 minutes
Therefore, it will take approximately 0.2 hours or 12 minutes for the water level in the tank to be filled by 7 cm.