a water tank is a cubiod with dimensions 40cm by 90cm by 70 cm. the tank is initially empty and is then filled with water which flows from a pipe of cross sectional area 1.2 sqcm at a speed of 3.5m/s. calculate the timein minutes that it takes to fill the tank completely.
well, the volume of water flowing in every second is
1.2cm * 350cm/s = 420 cm^3/s
Now divide the volume of the tank by the inflow rate to get the time (in seconds)
Well, let's break it down. First, we need to calculate the volume of the tank in cubic centimeters. So, we multiply the length, width, and height together: 40cm * 90cm * 70cm = 252,000 cubic centimeters.
Now, we have the flow rate of the water, which is 3.5 m/s, but we need it in cubic centimeters per second. Since the pipe has a cross-sectional area of 1.2 sqcm, we can multiply the flow rate by the cross-sectional area to get the volume flow rate: 3.5 m/s * 1.2 sqcm = 4.2 cubic centimeters per second.
To find the time it takes to fill the tank completely, we divide the volume of the tank by the volume flow rate: 252,000 cubic centimeters / 4.2 cubic centimeters per second = 60,000 seconds.
Finally, converting seconds to minutes, we have 60,000 seconds / 60 seconds per minute = 1,000 minutes.
So, it will take 1,000 minutes to fill the tank completely. Just enough time to watch a couple of episodes of your favorite TV show!
To calculate the time it takes to fill the tank completely, we first need to find the volume of the tank.
The volume of a cuboid is given by the formula:
Volume = length x width x height
Given:
Length (l) = 40 cm
Width (w) = 90 cm
Height (h) = 70 cm
Converting the dimensions to meters:
Length (l) = 40 cm / 100 = 0.4 m
Width (w) = 90 cm / 100 = 0.9 m
Height (h) = 70 cm / 100 = 0.7 m
Volume of the tank (V) = length x width x height
V = 0.4 m x 0.9 m x 0.7 m
V = 0.252 m³
Now, we can calculate the rate of flow of water into the tank.
Rate of flow of water (Q) = speed x cross-sectional area
Given:
Speed (v) = 3.5 m/s
Cross-sectional area (A) = 1.2 cm² = 1.2 cm² / (100 cm²/m²) = 0.012 m²
Q = 3.5 m/s x 0.012 m²
Q = 0.042 m³/s
Finally, we can calculate the time it takes to fill the tank completely by dividing the volume of the tank by the rate of flow of water:
Time (t) = Volume / Rate of flow
t = 0.252 m³ / 0.042 m³/s
t = 6 seconds
Since the question asks for the time in minutes, we need to convert seconds to minutes:
1 minute = 60 seconds
Time in minutes = 6 seconds / 60
Time in minutes = 0.1 minutes
Therefore, it takes 0.1 minutes (or 6 seconds) to fill the tank completely.
To calculate the time it takes to fill the tank completely, we need to find the volume of the tank and then determine the flow rate of the water from the pipe.
Step 1: Calculate the volume of the tank.
The volume of a cuboid can be calculated by multiplying its length, width, and height. In this case, the dimensions of the tank are 40 cm by 90 cm by 70 cm.
Volume = Length x Width x Height
Volume = 40 cm x 90 cm x 70 cm
Note: It's important to ensure that the units are consistent. In this case, the units are all in centimeters (cm), so the calculation can be done directly.
Step 2: Convert the units.
Since the flow rate is given in meters per second, we need to convert the volume of the tank from cubic centimeters to cubic meters.
1 cm³ = 1 × 10^(-6) m³ (conversion factor)
Volume = (40 cm x 90 cm x 70 cm) x (1 × 10^(-6) m³/cm³)
Step 3: Calculate the flow rate.
The flow rate can be determined by multiplying the cross-sectional area of the pipe (given as 1.2 sqcm) by the speed of the water (given as 3.5 m/s).
Flow Rate = Cross-sectional Area x Speed
Flow Rate = 1.2 sqcm x 3.5 m/s
Step 4: Calculate the time to fill the tank completely.
The time required to fill the tank can be obtained by dividing the volume of the tank by the flow rate.
Time = Volume / Flow Rate
Note: To ensure that the answer is in minutes, we need to convert the time from seconds to minutes by dividing it by 60.
Now let's calculate the time it takes to fill the tank completely:
1. Calculate the volume of the tank:
Volume = 40 cm x 90 cm x 70 cm = 252,000 cm³
2. Convert the volume from cubic centimeters to cubic meters:
Volume = 252,000 cm³ x (1 × 10^(-6) m³/cm³) = 0.252 m³
3. Calculate the flow rate:
Flow Rate = 1.2 sqcm x 3.5 m/s = 4.2 cm³/s
4. Calculate the time to fill the tank:
Time = Volume / Flow Rate = 0.252 m³ / 4.2 cm³/s
5. Convert the time from seconds to minutes:
Time = (0.252 m³ / 4.2 cm³/s) / 60 s/min
Now you can substitute the values and calculate the time.