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
- 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_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_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_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_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_forward4:30 O M docs.google.com/forms/d/e 1.25 rad/s 5 rad/s 2.5 rad/s 20 rad/s 10 rad/s A traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) = 0.1sin(4x+100t), where x and y are in meters and t is in seconds. The linear mass density of the string is u = 0.1 Kg/m. If the tension is multiplied by a factor of four, while keeping the same amplitude, same wavelength, and same linear mass density, then the new power of the wave, is 500 W 125 W 1000 W 2000 W 250 W Page 2 of 2 IIarrow_forwardProblem #2: A velocity distribution is given as V = Please calculate the work flux (Iv) associated with molecular motions. -bx8,-byô, + bz8, where b is a constant and b‡0.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_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_forwardConsider a hollow sphere of radii h and 3h, interior and exterior respectively. The mass density in the sphere is ρ = k / r, Kg / m³, where k is a constant, and r is the distance from the center of the sphere to an arbitrary point within it. If k = 3 m, find the gravitational field of the distribution at a point (P), on the x-axis, located at a distance of 4h, measured with respect to the center of the sphere. Ans: 5.655e-10arrow_forwardTaking U to be a function of P and V, derive the following equations: (), [), (a) đ = dP+ + P|dV. V Сук (b) V Cp Р. VB (c) - avarrow_forwardConsider the following linear equations,arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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