Quarts
There is more than one kind of quart:
One US liquid quart is 946ml: US liquid quart
One UK quart is 1.14L: UK quart
Barrels
It is important to note that there are different types of barrels used for different purposes:
The US liquid barrel is defined as 31.5 US liquid gallons, which is equivalent to about 119 liters: US liquid barrel
One US dry barrel is equivalent to 115.628 liters: US dry barrel
One oil barrel equaling approximately 42 US gallons or 159 liters: US Oil barrel
A Federal US Barrel typically contains 31 gallons, which is equivalent to approximately 117.35 liters: US federal barrel
One UK barrel is equivalent to around 164 liters: UK barrel