Pipes and Cisterns: Tank Filling Logic A pipe with a constant flow rate is connected from a tank to a vessel. The tank initially contains a certain amount of...
A pipe with a constant flow rate is connected from a tank to a vessel. The tank initially contains a certain amount of water, while the vessel is initially empty.
Flow rate and time:
The pipe can continuously fill the vessel as long as the flow rate of water into the tank is greater than the rate at which water drains out of the vessel.
As long as the flow rate is higher than the drain rate, water will continuously flow from the tank to the vessel.
The time taken for the tank to fill completely depends on the initial water level in the tank and the flow rate.
Filling process:
Initially, the water level in the tank is higher than the water level in the vessel.
Water starts flowing from the tank to the vessel at the rate of the flow rate.
As water flows in, the water level in the vessel gradually increases.
Eventually, the water level in the vessel reaches the same level as the water level in the tank.
The process continues until the tank is completely filled.
Key points to remember:
The flow rate of water is constant, while the drain rate depends on the water level in the tank.
The tank will always fill completely if the flow rate is higher than the drain rate.
The time taken for filling depends on the initial water level and the flow rate.
Examples:
Imagine a tank filled with water and a pipe connected to the tank. If the flow rate of water is higher than the drain rate, water will continuously fill the vessel.
Imagine a tank filled with water and a pipe connected to the tank. If the flow rate of water is lower than the drain rate, water will not fill the vessel completely