'm creating a project for a mixing tank with automatic dosing. I'm using an Arduino UNO and a 5V, 0.28A solenoid valve. My problem so far is that the Arduino pins only support 0.04A. Researching, the most practical solution I found was to use a transistor, in this case I already have a BC548. I would like to know if there is any theoretical calculation I can do to know if it will work or if it won't burn my Arduino.
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We need to see the data sheet on your solenoid valve (current, voltage, resistance).
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For something like this it is often recommended to use a logic level MOSFET.
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280mA is not that much current
The BC548 is limited to 100 mA absolute maximum collector current (Ic) and cannot handle the 280 mA solenoid current.
Choose a transistor that can comfortably handle at least Ic = 500 mA, and don't forget to use an inductive kick diode to protect the transistor as shown in the example circuit below:
On the transistor data sheet, the current gain is called "beta".
I didn't look at the datasheets but a beta of about 100 is not unusual. 0.04 x 100 is 4 Amps. Since your solenoid won't ever use 4-Amps (with the correct voltage) the transistor would be in "saturation". That's good! In switching circuits you want to saturate the transistor (or MOSFET) to turn it "fully on".
But you shouldn't really push the Arduino to it's limits so maybe calculate a base-resistor for 20mA or less.
Your topic has been moved as it does not indicate a problem with IDE 2.x.
The current gain is often defined by the last letter if the code bc547A, bc547b or bc547C.
A has lowest current gain, c has highest current gain.
A will not work for you, b might work for you, c issurely good enough.
All apart from the fact that 280 mA is too much.
If a transistor is used as a switch (reverse biased), then DC gain is irrelevant.
There should be enough base current, so collector voltage dips below base voltage.
The saturation graph in the datasheet could help you there.
A base:collector ratio of 1:20 is normal for small transistors, and 1:10 for medium powered ones (like the one in the diagram). Not enough base current will not fully saturate the transistor and overheat/damage it.
40mA is the absolute max for an Uno pin. 20mA is a safer limit.
A BC337 or 2N2222 could be better suited here.
Leo..
Edit: Just saw the 7.6A current rating of the motor.
Common bjt transistors struggle with > 500mA with 20mA base current.
The only option with this motor current is a logic level mosfet.
Have you looked at N-CH MOSFETs, more efficient.
If you have to purchase a transisitor(s), then MOSFET would be the best.
Tom.... 
I would suggest start using a simple relay module.