# Flow rate depending on pressure with constant inlet rate.

• blehxpo
In summary: Hint 2: Solve dV/dt = 0.In summary, a cylindrical water tank with an inlet at the top and a drain at the bottom has an outflow rate that depends on the absolute pressure at the bottom of the tank. The tank is open to atmosphere at the top and has a density of 1000kg/m^3. The inlet flow rate required to maintain a given water level can be calculated using the equation (10^-4)(P_atm + density*g*h). To keep the tank 50% full, an inlet flow rate of 15.03 kg/s is needed. To determine the time it takes for the tank to reach 30% full starting from empty, the out
blehxpo
A 10 m high, 5 diameter cylindrical water tank has an inlet at the top and a drain at the bottom. The flow rate out of the tank depends on the pressure at the bottom of the tank via the following:
dm/dt = (10^-4)*(P_bot)
where P_bot is the absolute pressure in Pascal at the bottom of the tank. The tank is open to atmosphere at the top (P_atm) The density of water is 1000kg/m^3

My Attempt:
a. What are the units of 10^-4
- If P_bot is in Pascals then it should just be [meter*second]

b.What is the absolute pressure at the bottom of the tank is psia when the tank is 50% full?

- P = P_atm + (density*g*h)
= 14.7 psi + (49000*145.04*10^-6) psi = 21.8 psi

c.What is the gauge pressure at the bottom of the tank is psig when the tank is 50% full?

- P_gauge = P_abs -P_atm
= 21.8-14.7 = 7.1 psi

d. At steady state, there is a specific inlet flow rate required to maintain a given water level in the tank.
Derive an equation that gives the inlet flow rate (in [kg/s]) required to maintain the water height (h) at a given level, where h [m] is measured from the bottom of the tank upwards.

inlet flow rate[kg/s] = outlet flow rate = F(h) = (10^-4)(P_atm + density*g*h)

e. Determine the inlet flow rate needed to keep the water level at 50% full.

10^-4(101325 Pa + 1000(9.8)(5m) = 15.03 kg/s

f. Assume that the tank is initially empty. At time t=0, the inlet is turned on at the flow rate you found in part (e). How long does it take the tank to reach 30% full.

This is where I got stuck.
I would assume inlet rate is constant at 15.03 kg/s. But I have no idea how to calculate the out flow rate.

g. How long does it take for the initially empty tank from part (f) to reach 50% full?

And I guess this is exactly like f.

blehxpo: Your answers are correct on items (a) through (e). On item (d), you might want to fill in the known numeric constants, but your choice.

(f) Hint 1: qout(h) = (1/rho)*Fout(h), where Fout(h) is the function you derived in item (d).
dV/dt = qin - qout(h).

## What is flow rate?

Flow rate is the volume of fluid that passes through a particular point in a given amount of time. It is typically measured in units such as liters per minute or cubic meters per second.

## How does pressure affect flow rate?

Pressure and flow rate have an inverse relationship, meaning that as pressure increases, flow rate decreases and vice versa. This is due to the fact that higher pressure can restrict the movement of fluid through a system.

## What is meant by constant inlet rate?

A constant inlet rate means that the fluid is entering the system at a steady and consistent rate. This is important to consider when studying the relationship between flow rate and pressure, as changes in inlet rate can also affect the flow rate.

## How can flow rate be measured?

Flow rate can be measured using various methods such as using a flow meter, timing the flow of a known volume of fluid, or using pressure sensors to calculate the flow rate based on pressure changes.

## What factors can affect the relationship between flow rate and pressure?

Aside from inlet rate, other factors that can affect the relationship between flow rate and pressure include the type and viscosity of the fluid, the size and shape of the system, and any obstructions or restrictions in the flow path.

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