Let's assume that we've somehow managed to solve the local pressure problem and can actually cause an erection that would significantly reduce a man's systemic blood pressure.
According to
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source, the average penis is 15cm long, 14cm in circumference, and requires 130mL of blood to become erect. I lack the wherewithal to dispute or fact check that, so let's go with those numbers.
For the sake of simplicity, we'll treat a penis as a perfect cylinder. The volume of a cylinder is given by the formula:
pi * radius squared * height
We don't have the radius, but we can calculate it from the circumference:
circumference = 2 * pi * radius
The radius of the average penis = circumference / 2 / pi =
14cm / 2 / 3.14 = 2.23cm
So the volume of the average penis is:
2.232 * 3.14 * 15 = 235 cubic centimeters.
Lucky for us, a cubic centimeter is exactly equal to one mL (thanks metric system!), so the ratio of blood to total volume in an erect penis is 130/235, or about 0.55.
The average adult male has about 5 liters of blood (don't ask me how I know this), and the body's compensatory mechanisms can keep a person conscious until they lose about 20% of that volume, or one liter. For a person to pass out from an erection, their penis would have to hold one liter of blood. Using the ratio from above, that penis would have a total volume of 1.82 liters, or 1,820 mL.
Using the same ratio of length to radius as above (about 6.75), we can calculate length and girth with simple substitution.
volume = r2 * pi * height
1820 = r2 * pi * 6.75r
86 = r3
r = 4.4cm
h = r * 6.75 = 30cm
So, a penis 30cm (11.8 inches) long and 8.8cm (3.5 inches) wide would be able to hold enough blood to make the average man pass out.