Parachutes: Does the size of parachutes effect the speed of it?

Yes it does.

A parachute works by creating drag on a load or person falling through the air. It does this by presenting a large surface area in the direction that the load is moving (downwards) and causing enough air resistance to slow the rate of descent to the point where the person or load can eventually touch down on the ground unharmed.

There is a complicated equation for this question.

We will use the drag force, or "wind resistance force" equation, which is

FD = ½ r Cd A v2

Where
FD is the drag force
r (Greek letter "rho") is the density of air = 1.22 kg/m3
Cd is the drag coefficient
A is the area of the chute
v is the velocity through the air

Meanwhile, the weight of the objectt, otherwise known as the force of gravity (FG), is computed to be

FG = m g

Where
m is the mass of the object
g is the acceleration of gravity = 9.81 m/s2

Let's find when they're equal:

FG = FD
m g = ½ r Cd A v2

...and solving for chute area...

A = (2 m g) / (r Cd v2)

Now the chute area, in terms of the chute diameter, is A = p D2 / 4, so the chute diameter is

D = sqrt(4 A / p).

The Answer
Combining the two equations above for A & D leads us to the final form of the chute equation as we will use it:

D = sqrt( (8 m g) / (p r Cd v2) )


Finding Descent Velocity
Note that we can easily find the descent velocity, given the chute diameter, with the following equation
v = sqrt( (8 m g) / (p r Cd D2) )