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+APPS
- 4. Suppose an xy-coordinate system is located in space such that the temperature T at the point (x ; y) is given by T =00. Determine the gradient of T with x²+y2 respect to the distance at the point P(1; 3), use the gradient to find the directional derivative of T at P in the direction of a = i – j and then calculate the rate of change of T in this direction.arrow_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_forwardTp = Fq +°P/Q• (1) Here ip/Q is the "position of point P relative to point Q." Similarly the velocities of the two points are related by õp = bq + Up/Q- (2) The quantity õp/Q is the velocity of point P relative to point Q. I want you to use these ideas to solve the following problems. 1. The figure below shows a view from above of a large boat in the middle of the ocean. So that the crew on the ship can get exercise on long journeys, there is a circular walking/running track on the back deck. CA B- -D Suppose that the radius of the track is R = 6 m, and a person is running on the track at a constant speed of v = 3m/s as measured with a stopwatch by a crew-mate on board the ship. Suppose the runner is running counter-clockwise around the track when viewed from above. Write the velocity vector of the runner in terms of basis (ê1, ê2) as perceived by a crew-mate on the ship. (a) What is the velocity vector when the runner is at point A? (b) What is the velocity vector when the runner is…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_forward
- Let f be any non-zero real valued function in x and y and R be a closed bounded region above the x-axis. Then the double integral of f over R is always positive * False Truearrow_forwardConstants I Periodic Table A cylindrical pipe has inner radius R1 and outer radius R2 . The interior of the pipe carries hot water at temperature T1. The temperature outside is T, (< T1). Suppose the pipe is steel with R1 of its temperature? = 3.3 cm , R2 = 4.2 cm , and T2 = 18 °C. If the pipe holds still water at Ti = 70 ° C, what will be the initial rate of change Express your answer using two significant figures. Πν ΑΣφ dT °C/s dt Previous Answers Request Answer Submit X Incorrect; Try Again; 8 attempts remaining Part C Suppose water at 70 °C enters the pipe and moves at a speed of 8.4 cm/s . What will be its temperature drop per centimeter of travel? Express your answer using two significant figures. nνα ΑΣφ dT °C/cm dx Request Answer Submitarrow_forwardPlease answer this question correctly used the parametric equation thx(vector integral) 1 a.) Find the curve of the vector : XZ⁴i-ZX⁴K b.) Find the derivative directed f at point P in the direction of a F= XY+YZ+25 P= (-2,4,7) a= -i+j+5Karrow_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_forwardi need the answer quicklyarrow_forward
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