Consider the angular momentum relation in the form
What does r mean in this relation? Is this relation valid in both solid and fluid
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Fluid Mechanics
- (b) if Vr = U, thên vg J(r). Q2 Determine the velocity profile in a fluid situated between two coaxial rotating cylinders. Let the inner cylinder have radius R1, and angular velocity N1; let the outer cylinder have radius R2 and angular velocity N2.arrow_forwardChoose from the list below the correct equations that correspond to the balance of linear momentum (BoLM) and the balance of angular momentum (BOAM) for an incompressible hyperelastic material with stored energy function W. BOLM: Poö = V · (DW(F) – pJF-T) + pofm BOAM: always satisfied None of the above BOLM: Poö = V · (DW (F) – pJF-")+ pofm BOAM: SR = SR BOLM: Poë = V · DW (F)+ pofm BOAM: always satisfiedarrow_forwardOne of the oldest equations in fluid mechanics deals with the flow of a liquid from a large reservoir. Using the Bernoulli equation along the streamline, (a) find out the velocity in m/s at the exit (location (2)) when h = 20 m and (b) find out the velocity in m/s at the location (5) for H = 4 m. Here the gravitational acceleration (g) can be approximated to be 10 m/s². h 147 H d (5) • (1) (3) (2) (4)arrow_forward
- Water with density of 1000 kg/m^3 flows through a horizontal pipe (in the x-z plane) bend as shown. The weight of the pipe is 350 N and the pipe cross-sectional area is constant and equals to 0.35 m^2. The magnitude of the inlet velocity is Section (1) 4 m/s. The absolute pressures at the entrance and exit of the bend are 210 kPa and 110 kPa, respectively. Assuming the atmospheric pressure is 100 kPa and neglecting the weight and viscosity of the water , find the following: Control volume The mass flow rate is 180° pipe bend Section (2) The exit velocity is The force (in the z-axis direction) acting on the fluid isarrow_forwardQ4: Oil was placed over water placed in a tube in the shape of the letter A, so it moved the air on the other side, as in the figure below. Find the height of the column of air, and if it passes through the left tube, what is its velocity, knowing that the air density is 1.29 kg/m³ and the density of the oil is 750 kg/m³? Patm Patm air h L = 5 cm -K Point B Poin: A water oilarrow_forwardA piston compresses gas in a cylinder by moving at constantspeed V , as in Fig. P4.18. Let the gas density andlength at t = 0 be ρ 0 and L 0 , respectively. Let the gas velocityvary linearly from u = V at the piston face to u = 0 atx = L . If the gas density varies only with time, fi nd anexpression for ρ ( t ).arrow_forward
- 3. 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_forwardLet's say that the semiempirical binding energy formula is Eb= aA-bA^2/3 - s(N-Z)^2/A -dZ^2/A^1/3 where a,b,s,d are constants. Imagine that you are in a different universe where there are 3 types of nucleons with spin equal to 1/2 and electric charges equal to +1, -1 and 0. Mass similar to that of a proton. Forces are similar to those of our universe. i) How do equations change for A and Z as a function of N+, N-, No and what is the semiempirical equation for the binding energy as a function of A, Z, and No? ii) At what Z and No do we have the maximum and minimum binding energy for every A? iii) When do we have stable nuclei under beta (β) decay? If "alpha particle" in this situation has N+ = N- = No = 2, what does apply for alpha (α) decay? iv) What does apply for nuclear fission and finally, how would life be in this situation?arrow_forwardThis is a dynamics question. Answer: vB = 24.1 m/sarrow_forward
- Q2. In the one-dimensional constant-density situation below, the momentum equations for UB and u can be written as follows: Ug = 5+2.5(P₁-P₂) uc=5+7.5(P₂ - P3) U₁ A UB B uc с 2 The boundary conditions are as: ug =15, P3 = 10 (all values are given in consistent units). (i) (ii) Write the continuity equations for the regions AB and BC and hence derive the corresponding pressure correction equations. Starting with guesses for p, and p₂, follow the SIMPLE procedure to obtain converged values of P₂,ug and uc.arrow_forwardA piston moves with constant velocity U0 in a cylinder having radius R. A liquid having density leaves the open end with conical velocity proÖle V~ = V0(1-r/R)^k.Figure for problem 1.(a) If the exhaust port is closed, find the value of V0 in terms of U0. Be sure to define an appropriate control volume for solving this problem.(b) If V0 = U0, find the volume áow rate leaving through the exhaust port (in terms of U0 and R)arrow_forwardWater at T = 20°C rotates as a rigid body about the z-axis in a spinning cylindrical container. There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface (zsurface as a function of r).arrow_forward
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