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
- In mechanical fluidarrow_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_forward4. 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_forward
- Ձ Ա 12h fluid with f. **>x u Figure 1: Parallel Plates, top plate moving to the right at 2U and the bottom plate moving to the left at U. / ני ди suly)=? Figure 2: Angled Plate with a free surface 3. Figure 1 shows two infinite parallel plates separated by a distance 2h where the top plate is moving at a velocity 2U to the right and the bottom plate is moving to the left at a speed U. Noting that the coordinate system starts at the midpoint between the plates find the following: (a) Use continuity and boundary conditions to show v = 0 everywhere. (b) Derive the velocity profile u (y) using Navier-Stokes Equation. (c) At what position between the two plates is u (y) = 0?arrow_forwardnavier stokesarrow_forwardConsider 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_forward
- Please try to answer the question within 25-30 minutesarrow_forwardA 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_forwardA solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by 15 – 9(x2 + y + z?) °C. Use the fact that heat flow is given by the vector field F w(x, y, z) -KVw and the rate of heat flow across a surface S within the solid is given by -K s Vw dS. Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper (K 400 kW/(m · K)). (Use symbolic notation and fractions where needed.) -K Vw dS = kWarrow_forward
- Tp = 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_forwardProblem 1 Show that if the following problem has a solution it is unique -k = f in (0,L)× (0,T), (1) u(0,t) = g,(t),"(L,t) = g,(t),0arrow_forwardLet 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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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