To be dimensionally consistent, pressure [M/LT2], density [M/L3], and velocity [L/T] must be related as follows.

Select one:
a. pressure = density ´ velocity2
b. pressure = density2 ´ velocity
c. pressure = density ´ velocity
d. pressure2 = density ´ velocity2

Well, it seems like we have a dimensional consistency conundrum! Let's break it down with a touch of humor, shall we?

Let's start with option a. Pressure equals density times velocity squared. Ah, the quadratic action of velocity, causing a pressure party! But alas, it doesn't quite add up.

Moving on to option b. Pressure equals density squared times velocity. Oh, the power of density squared! But alas, it's not the correct equation.

What about option c? Pressure equals density times velocity. Ah, a simple and elegant relationship. No need for fancy squares or cubes, just good ol' multiplication. It's looking promising!

Lastly, we have option d. Pressure squared equals density times velocity squared. Oh, the suspense! Squaring both sides of the equation can surely lead to a twist ending.

After some humorous analysis, I can confidently say that the correct answer is option c. Pressure equals density times velocity. That's the equation that keeps the dimensions in harmony!

The correct answer is a. pressure = density ´ velocity^2

To determine the relationship between pressure, density, and velocity to ensure dimensional consistency, we need to analyze the units of each quantity.

Pressure is measured in units of mass per unit area per unit time (M/LT^2).
Density is measured in units of mass per unit volume (M/L^3).
Velocity is measured in units of length per unit time (L/T).

To find a correct relationship, we can start by examining the units on each side of the equation.

a. pressure = density ´ velocity^2
The units on the right side of the equation are (M/L^3) * (L^2/T^2) = M/(L*T^2). This is not equal to the units of pressure (M/LT^2), so option a. is incorrect.

b. pressure = density^2 ´ velocity
The units on the right side of the equation are (M/L^3)^2 * (L/T) = M^2/(L^6T). This is not equal to the units of pressure (M/LT^2), so option b. is incorrect.

c. pressure = density ´ velocity
The units on the right side of the equation are (M/L^3) * (L/T) = M/(L^2T). This is equal to the units of pressure (M/LT^2), so option c. is a possible correct answer.

d. pressure^2 = density ´ velocity^2
The units on the left side of the equation are (M/LT^2)^2 = M^2/(L^2T^4), and the units on the right side of the equation are (M/L^3) * (L^2/T^2) = M/(L*T^2). These units are not equal, so option d. is incorrect.

In conclusion, the correct answer is c. pressure = density ´ velocity.

LOL, well we all know that pressure is density * v^2 but we better answer the question anyway.

pressure = force/area

= mass * acceleration / area^2

= M L/T^2 / L^2 = M /(L T^2)

density = M/L^3

velocity = L/T

so
density * velocity^2 = M/L^3 *L^2/T^2
= M (L T^2)
which sure enough is the pressure units