Initial volume rate must equal final volume rate:

Solving for

Plugging in values:

We can model the volumetric flow through the tube as the following expression:

Where:

so:

Applying this to the first and second scenario, we get:

According to the law of continuity, we know that the volumetric flow through the tube (when neglecting friction and assuming that it is horizontal) is constant. Therefore, we can say:

Rearranging for the ratio :

From the problem statement, we are told that the circumference is doubled. Thus, we know that the radius of the tube doubles as well:

Plugging this into the expression, we get:

By decreasing the diameter of the pipe we increase the volume flow rate, or the velocity of the fluid which passes through the pipe according to the continuity equation. 

Increasing or decreasing the length of the pipe has no effect on fluid velocity. Therefore the correct answer is to decrease the diameter of the pipe.

The velocity of the fluid in the compressed section will increase and the The pressure of the fluid in the compressed section will decrease. Therefore the correct answer is: More than one of these is true.

When the area of a pipe decreases the fluid velocity increases, and an increase in fluid velocity results in the decrease of pressure.

Initial volume rate must equal final volume rate

Solving for :

Plugging in values:

The equation for determining the velocity of fluid through a hole is as follows:

This equation is actually derived from Bernoulli's principle. The  is for velocity, the  is the acceleration due to gravity and  is the height. We solve for velocity by substituting for the values:

The correct answer is  because the cross-sectional area of the syringe is  times larger than the needle opening. Therefore, the velocity will be  larger as well. 

The continuity equation says that the cross sectional area of the pipe multiplied by velocity must be constant. Let  be the water speed in pipe .

Flow rate is equal to the product of cross-sectional area and velocity and must remain constant. Therefore, as the cross-sectional area decreases, the velocity increases.

We need Bernoulli's equation to solve this problem:

The problem statement doesn't tell us that the height changes, so we can remove the last term on each side of the expression, then arrange to solve for the final pressure:

We know the initial pressure, so we still need to calculate the initial and final velocities. We'll use the continuity equation:

Rearrange for velocity:

Where  is the cross-sectional area. We can calculate this for each diameter of the tube:

Now we can calculate the velocity for each diameter:

Now we have all of the values needed for Bernoulli's equation, allowing us to solve: