Correct Bernoulli's equation is (symbols have their usual meaning) :

<p>Bernoulli's equation relates the pressure, velocity, and height in a flowing fluid and is derived from the principle of conservation of energy. The correct form of Bernoulli's equation is:</p> <p>$P + \rho g h + \frac{1}{2} \rho v^2 = \text{constant}$</p> <p>where:</p> <ul> <li><b>P</b> is the pressure within the fluid.</li> <li><b>$\rho$</b> is the density of the fluid.</li> <li><b>g</b> is the acceleration due to gravity.</li> <li><b>h</b> is the height above a reference point.</li> <li><b>v</b> is the velocity of the fluid.</li> </ul> <p>Looking at the options given:</p> <ol> <li>Option A: $P + \frac{1}{2} \rho g h + \frac{1}{2} \rho v^2 = \text{constant}$</li> <li>Option B: $P + m g h + \frac{1}{2} m v^2 = \text{constant}$</li> <li>Option C: $P + \rho g h + \rho v^2 = \text{constant}$</li> <li>Option D: $P + \rho g h + \frac{1}{2} \rho v^2 = \text{constant}$</li> </ol> <p>Option D correctly represents Bernoulli's equation in its proper form. Therefore, the correct answer is:</p> <p><b>Option D</b></p>