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 this 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.