# Filling a tank flow rate problem

• robert.hare
The equation being used is q = d^2 * v * pi /4, where d is the diameter of the hole in meters and v is the velocity of water in meters per second, calculated as (2*9.8*height)^.5. The problem is to plot the equation on an x and y axis to find the derivative, f'(x), which represents the flow rate in cubic meters per second at any point in the tank as it becomes full. In summary, the conversation discusses using an equation to calculate the flow rate of water entering a ship's tank and the problem of plotting the equation to find the derivative at any point in the tank.
robert.hare
Goodday I wonder if anyone can help , I have a problem with an equation where a ships tank floods from sea water ingress .
I use the equation q= d^2 * v * pi /4 where
d = diametre of hole in m
v = velocity of water m/s as ( 2*9.8*height)^.5
My problem is how do i plot the on an x and y to find the f'(x) where i can see at any point in the tank becoming full , what will the flow rate be in m^3 /sec
thanks
rob

??What is q? What is f? How are they related?

q = flow rate and f is the function

## 1. What is a "filling a tank flow rate problem"?

A "filling a tank flow rate problem" is a mathematical problem that involves calculating the rate at which a tank is being filled with a liquid or gas. It typically involves determining the time it takes to fill the tank or the amount of liquid or gas that can be filled in a given amount of time.

## 2. How do you calculate the flow rate of a tank?

The flow rate of a tank can be calculated by dividing the volume of liquid or gas that is being added to the tank by the time it takes to fill the tank. This can be represented by the equation: flow rate (L/min) = volume (L) ÷ time (min).

## 3. What factors can affect the flow rate of a tank?

The flow rate of a tank can be affected by several factors, including the size and shape of the tank, the type of liquid or gas being filled, the pressure and temperature of the liquid or gas, and any obstructions or restrictions in the filling process.

## 4. How can you increase the flow rate of a tank?

The flow rate of a tank can be increased by using a larger or more efficient filling mechanism, increasing the pressure or temperature of the liquid or gas being filled, and minimizing any obstructions or restrictions in the filling process.

## 5. What are some real-life applications of "filling a tank flow rate problems"?

Filling a tank flow rate problems have many practical applications, such as determining the rate at which a gas tank is being filled at a gas station, calculating the time it takes to fill a swimming pool, or determining the flow rate of a chemical being added to a storage tank in a manufacturing plant.

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