A rectangular water tank measures 2.4m long, 2m wide and 1.5m high. The tank contained some water up to a height of 0.45m
(a) calculate the amount of water, in litres, needed to fill up the tank.
vol = 2.4*2* 1.5- 2.4*2*0.45
=7.2 - 2.16
= 5.04*1000
= 5040L
(b) An inlet pipe was opened and water let to flow into the tank at a rate of 10 litres per minute. After one hour, a drain pipe was opened and water allowed to flow out of the tank at a rate of 4 litres per minute.
(i) the height of water in the tank after 3hours
(ii) the total time taken to fill up the tank
0.68m
empty space volume is 2.4*2*(1.5-0.45) = 5.04 m^3 = 5040L
you are correct
So, initially, there were 2.16 m^3 = 2160L in the tank
during the first hour, 10L/min * 60min = 600L flowed into the tank.
when the valve was opened, the net fill rate was 10-4 = 6L/min
volume after 3 hours was 600 + 6*2*60 L
total minutes to fill was 60 + (5040-600)/6 minutes
(i) To calculate the height of water in the tank after 3 hours, we need to consider the rate of water being added and the rate of water being drained.
Rate of water being added: 10 litres per minute
Rate of water being drained: 4 litres per minute
After 3 hours, the total time taken is 3 hours * 60 minutes per hour = 180 minutes.
The net rate of water entering the tank is 10 litres per minute - 4 litres per minute = 6 litres per minute.
Therefore, the total amount of water added in 3 hours is 6 litres per minute * 180 minutes = 1080 litres.
The initial height of water in the tank was 0.45 meters, so the final height will be:
Final height = initial height + (volume added / base area)
The base area of the tank is 2.4 meters * 2 meters = 4.8 square meters.
Final height = 0.45 meters + (1080 litres / 4.8 square meters)
(ii) To calculate the total time taken to fill up the tank, we need to consider the rate of water being added.
The rate of water being added is 10 litres per minute.
The total volume of the tank is 2.4 meters * 2 meters * 1.5 meters = 7.2 cubic meters.
To convert from cubic meters to litres, we multiply by 1000.
Total volume in litres = 7.2 cubic meters * 1000 = 7200 litres.
The total time taken to fill up the tank is:
Total time taken = Total volume in litres / rate of water being added
Total time taken = 7200 litres / 10 litres per minute
Note: Please note that this calculation does not take into account the drain pipe, which will affect the total time taken.
To answer the given questions, we'll need to calculate the change in water level in the tank over time.
First, let's calculate the rate of water inflow and outflow:
- Inflow rate: 10 liters per minute
- Outflow rate: 4 liters per minute
Since the inflow rate is greater than the outflow rate, the water level in the tank will increase.
Now let's proceed to answer the questions:
(i) To calculate the height of water in the tank after 3 hours, we need to consider the total water inflow and outflow during this time.
Total inflow during 3 hours:
10 liters/minute * 60 minutes/hour * 3 hours = 1800 liters
Total outflow during 3 hours:
4 liters/minute * 60 minutes/hour * 3 hours = 720 liters
Net change in the water level:
1800 liters - 720 liters = 1080 liters
To find the height of water, we'll divide the net change in volume by the base area of the tank. The base area is calculated by multiplying the length and width of the tank.
Height of water = Net change in volume / Base area
Base area = 2.4 meters * 2 meters = 4.8 square meters
Net change in volume = 1080 liters
Now, we need to convert the liters into cubic meters since we are dealing with meters for the height:
1080 liters = 1080/1000 cubic meters = 1.08 cubic meters
Finally, we can calculate the height of water in the tank after 3 hours:
Height of water = 1.08 cubic meters / 4.8 square meters = 0.225 meters
Therefore, the height of water in the tank after 3 hours is 0.225 meters.
(ii) To find the total time taken to fill up the tank, we need to calculate the time required to fill the remaining volume of the tank.
Remaining volume = Total volume of the tank - Initial volume of water
Total volume of the tank = Length * Width * Height = 2.4 meters * 2 meters * 1.5 meters = 7.2 cubic meters
Initial volume of water = Length * Width * Initial water height = 2.4 meters * 2 meters * 0.45 meters = 2.16 cubic meters
Remaining volume = 7.2 cubic meters - 2.16 cubic meters = 5.04 cubic meters
Dividing the remaining volume by the inflow rate:
Time to fill up remaining volume = Remaining volume / Inflow rate = 5.04 cubic meters / 10 liters per minute = 504 minutes
Therefore, the total time taken to fill up the tank is 504 minutes.