Which of the following is a direct result of the equation of continuity?

a. The pressure one meter below the surface of water is about 10% greater than atmospheric
pressure.
b. The pressure on the inlet side of a horizontal pipe through which water is flowing at
constant speed equals the pressure on the outlet side.
c. When the open end of a long evacuated tube is inserted into a pool of water, water rises to
about 10 m in the tube.
d. Placing your thumb partially over the opening of a hose causes the velocity of the water
leaving the hose to increase.
e. None of the above.

I believe B,C, and D are correct but not A. gauge pressure is = Density*gravity*depth, which comes out to be 9800 PA. This isn't anywhere close to 10% of atmospheric pressure.

Nope, Devron.

Lets look at A. If normal atmospheric pressure is 10m of water, then 1m below the surface of water adds about 10percent to the pressure.

B. constant speed? True. that means the area on the inlet is the same as the area of the outlet. This neglects friction,..
C. true
d. true, every schoolkid has done this in the summer.

You are correct.

You're in for a treat because the answer is e. None of the above! The equation of continuity states that the product of the cross-sectional area and the fluid velocity at one point in a pipe must be equal to the product of the cross-sectional area and the fluid velocity at any other point in the pipe. So it's all about flow rates, my friend, not about pressures or rising water levels or thumb trickery. Keep the humor flowing like a well-constructed pipe!

The equation of continuity is a fundamental principle in fluid dynamics that states that the mass flow rate of an incompressible fluid through a given section of a pipe or channel is constant.

To determine which of the options is a direct result of the equation of continuity, we need to understand the concept.

The equation of continuity is expressed as:

A1v1 = A2v2

where A1 and A2 are the cross-sectional areas of the pipe or channel at two different points, and v1 and v2 are the velocities of the fluid at those points.

Let's analyze each option and see if it follows from the equation of continuity:

a. The pressure one meter below the surface of water is about 10% greater than atmospheric pressure.
The equation of continuity does not provide any information about pressure changes in a fluid. Therefore, option a is not a direct result of the equation of continuity.

b. The pressure on the inlet side of a horizontal pipe through which water is flowing at a constant speed equals the pressure on the outlet side.
According to the equation of continuity, if the fluid is flowing at a constant speed (which implies constant velocity), and the pipe is horizontal (no change in elevation), the pressure on the inlet side should be equal to the pressure on the outlet side. Therefore, option b is a direct result of the equation of continuity.

c. When the open end of a long evacuated tube is inserted into a pool of water, water rises to about 10 m in the tube.
The equation of continuity does not provide any information about the rise of water in a tube. This situation is related to the equilibrium between the atmospheric pressure acting on the water surface and the pressure exerted by the column of water in the tube. Therefore, option c is not a direct result of the equation of continuity.

d. Placing your thumb partially over the opening of a hose causes the velocity of the water leaving the hose to increase.
The equation of continuity states that the product of the cross-sectional area and the velocity of the fluid at any given point is constant. When you partially block the opening of a hose with your thumb, the cross-sectional area decreases, which leads to an increase in the fluid's velocity to maintain the continuity equation. Therefore, option d is a direct result of the equation of continuity.

Based on the analysis, the correct answer is:

b. The pressure on the inlet side of a horizontal pipe through which water is flowing at constant speed equals the pressure on the outlet side.
d. Placing your thumb partially over the opening of a hose causes the velocity of the water leaving the hose to increase.

Therefore, the answer is (b) and (d).