Bissoy.com
Doctors Medicines MCQs Q&A

Euler’s equations of motions can be integrated when it is assumed that

Euler’s equations of motions can be integrated when it is assumed that Correct Answer A velocity potential exists and the density is constant.

​Explanation:

Euler's equation of motion:

Euler's equation for a steady flow of an ideal fluid along a streamline is a relation between the velocity, pressure, and density of a moving fluid. It is based on Newton's Second Law of Motion which states that if the external force is zero, linear momentum is conserved. The integration of the equation gives Bernoulli's equation in the form of energy per unit weight of the following fluid.

It is based on the following assumptions:

  • The fluid is non-viscous (i,e., the frictional losses are zero)
  • The fluid is homogeneous and incompressible (i.e., the mass density of the fluid is constant)
  • A velocity potential exists.
  • The flow is continuous, steady, and along the streamline.
  • The velocity of the flow is uniform over the section.
  • No energy or force (except gravity and pressure forces) is involved in the flow.

As there is no external force applied (Non-viscous flow), therefore linear momentum will be conserved.

Related Questions

National Curriculum Framework, 2005 recommends that teaching-learning of mathematics in primary classes needs to follow an integrated approach which implies that (a) mathematics needs to be integrated with problem-solving. (b) mathematics needs to be integrated with a child's experiences inside and outside the classroom. (c) mathematics needs to be integrated with other subjects like Environmental Science and Language. (d) mathematics need not be integrated with higher mathematics.
Considering the problem of (linear) bending of beams according to the Euler-Bernoulli beam theory, if the beam is in equilibrium, then solving the equations governing the equilibrium of the Euler-Bernoulli beam is equivalent to minimizing the total potential energy.
Two simple motions are represented by y1=5(sin2πt+√3 cos2πt) y2=5sin⁡(2πt+π/4) The ratio of the amplitude of two simple harmonic motions is?
The major difference between the Navier-Stokes equations and the Euler equations is the dissipative transport phenomena. The impact of this phenomena in a system is ____
In order to apply Bernoulli’s equation across two sections, we have to obtain it from Euler’s equation. What is the operation that needs to be carried out in order to obtain it from Euler’s equation?
While numerically solving the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{x}}{{\text{y}}^2} = 0,\,{\text{y}}\left( 0 \right) = 1$$     using Euler's predictor-corrector (improved Euler-Cauchy) with a step size of 0.2, the value of y after the first step is
The velocity v (in m/s) of a moving mass, starting from rest, given as $$\frac{{{\text{dv}}}}{{{\text{dt}}}} = {\text{v}} + {\text{t}}{\text{.}}$$   Using Euler forward difference method (also known as Cauchy-Euler method) with a step size of 0.1 s, the velocity at 0.2 s evaluate to
According to Euler's column theory, the crippling load of a column is given by $${\text{p}} = \frac{{{\pi ^2}{\text{E}}I}}{{{\text{C}}{l^2}}}.$$   In the Euler's formula, the value of C for a column with one end fixed and the other end free, is
In the following question, two statements are given each followed by two conclusions I and II. You have to consider the statements to be true even if theyseem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements. Statements:
(I) Some polynomials are linear equations.
(II) Some linear equations are quadratic. Conclusion:
(I) Polynomials are quadratic.
(II) Linear equations are quadratic.
The figure shows the plot of y as a function of x
Differential Equations mcq question image
The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is