In modified Bernoulli equation (P = 4V ²), from where did the number 4 came ?

Bernoulli equation is the most critical equation on which the foundation of clinical Doppler echocardiography is built. Bernoulli equation tells about fluid mechanics. Bernoulli’s principle states that the sum of potential and the kinetic energy of a fluid per unit volume flowing through a tube is constant. A more detailed explanation regarding Bernoulli equation is linked in this video Applying Bernoulli in Echocardiography So,  if we can somehow measure the velocity gained across a point inside the heart we can deduce the pressure gradient. Here comes the Doppler principle that helps us calculate the velocity. Doppler is based on the reflection of sound and the Doppler shift. With the Doppler shift, we can arrive difference in velocity across a valve, or conduit. When fluid flows across a narrowed orifice (Valve /Outflow) it accelerates and builds up velocity. This gain in velocity is equal to the pressure lost ie as given by the Bernoulli equation. Since potential energy is related to height and gravity same intracardiac zones it cancels out on either side. Hence, essentially the Bernoulli pressure gradient is equal to the difference between the kinetic energy on either side. Let us see how this  1/2 of mass becomes 4.  We have to convert  density of blood which is 1.060 to mass. Note : Mass = ρV . Density is mass per unit volume. So the “m” in the equation is some times referred to synonymously with the density of blood.   Application in cl...
Source: Dr.S.Venkatesan MD - Category: Cardiology Authors: Tags: Uncategorized .Bernoulli equation in echocardiography 4 is the constant in modified bernouli equation from doppler and bernouli mass of blood vs density of blood what is four in Bernoulli equation Source Type: blogs