Which choice is the genera1 differential equation form of the continuity equation for a control volume?
- None of these
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Fluid Mechanics: Fundamentals and Applications
- Numerical analysisarrow_forwardA higher-order differential equation given as y" + p(x)y' g (x)y = O is a homogenous equation, even if p(x) = 0. A higher-order differential equation given as y" + p(x)y' + q(x)y = 0 is also a homogenous equation, even if g(x) = 0. O Only first statement is true. O Only second statement is true. O Both first and second statements are true. O Both first and second statements are false.arrow_forwardnavier stokesarrow_forward
- Consider the mechanical energy equation: P + VB? + gzB =PA + V? + g ZA + w – loss A +g ZA + W – loss where loss 2 0 Select ALL true statements below. a fluid particle will flow through point A before point B a fluid particle will flow through point B before point A points A and B do not lie on the same streamline if a turbine is present, w < 0 if a pump is present, w < 0 if the fluid is perfectly inviscid, loss can be 0arrow_forwardMechanical EngineeringFluid Mechanicsarrow_forwardPlease try to answer the question within 25-30 minutesarrow_forward
- A differential equation in the form 2 points of y' + P(x)y = Q(x) y^n is separable when n = O. If n = 1, then it is a Bernoulli equation. O Only the second sentence is true O Both first and second sentences are true O Only the first sentence is true. ( Both first and second sentences are false.arrow_forwardHome Work (steady continuity equation at a point for incompressible fluid flow: 1- The x component of velocity in a steady, incompressible flow field in the xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find the simplest y component of velocity for this flow field. 2- The velocity components for an incompressible steady flow field are u= (A x* +z) and v=B (xy + yz). Determine the z component of velocity for steady flow. 3- The x component of velocity for a flow field is given as u = Ax²y2 where A = 0.3 ms and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Assume incompressible steady two dimension flowarrow_forward3. The stress tensor of a fluid in motion is given by -P T1 T2 -P 0 T = T1 T2 0 -P] where P, ti and t2 are known. (a) Find an expression to calculate the force exerted by the fluid on surfaces with surface area A that are perpendicular to the unit vectors (a.1) n = ei √2 √2 (a.2) n = ²е₁ + ¹²е₂ (b) What are the normal stresses acting on the two surfaces specified above?arrow_forward
- key values :- Note this values my be positive or negative A is 2 B is 20 only HANDWRITTEN answer needed ( NOT TYPED)arrow_forward3.5 Consider the steady, incompressible blood flow through the vascular network as shown. Determine the magnitude and the direction of the volume flow rate through the daughter branch 2 (denoted as d3 in Figure 3.25). The velocity at location 1 is inflow and the velocity at location 2 is outflow. d, 100 μm = V₁ = 100 mm/s FIGURE 3.25 Figure for Homework Problem 3.5. d₂ = 35 μm d₂=75 μm V₂80 mm/sarrow_forwardThe continuity equation of fluids describes the property of energy conservation; and Bernoulli's equation indicates conservation of mass. Ture OR Falearrow_forward
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