HW_4_Soln

HW_4_Soln - ME 309 Fall 2008 Section 2(Merkle Homework 4...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ME 309 Fall 2008 Section 2 (Merkle) Homework # 4 Due Fri. 5 September 2008 Problem 4-1. Water enters a garden-hose nozzle with an average velocity of 1.8 m/s . The diameter at the nozzle entrance is 15 mm . The nozzle is open such that the effective flow area at the exit is an annulus with outer and inner diameters of 6 mm and 5 mm , respectively. What is the average water velocity at the exit annulus? SOLUTION: Known : V in , D in , D out,eff Find: V out Sketch : Assumptions: Use conservation of mass Fluid is incompressible Constant and uniform fluid properties Steady State Solution : Apply conservation of mass principle: dt dM m m m CV gen out in = + - Third and fourth terms are zero: 0 = - out in m m out out out in in in A u A u ρ = properties are constant—density is constant ( ) 2 2 2 005 . 0 006 . 0 * / 015 . 0 * 8 . 1 / - = = π in in out A u u = 36.82 m/s Problem 4-2 . Consider a cylindrical tank with a diameter D of 1.0 m and a height H of 1.5 m as shown on the sketch. Water ( ρ = 1000 kg/m 3 ) enters the tank at the bottom through a tube with diameter d of 5 mm at a constant average velocity of 4 m/s. Initially (time t = 0), the tank is half full as shown; water continues to enter until the tank begins to overflow at time t full . Selecting the water inside the tank at any instant as the control volume of interest, write or Sketch of Cylindrical Tank
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
develop a formal explicit expression of mass conservation for this control volume. Your result should be in the form of an ordinary differential equation. Solve your differential equation for t full and determine a numerical value using the data given. SOLUTION: Known : Cylindrical tank, D, H, ρ , d , u in Find : t full Sketch : Above Assumptions : Constant inlet velocity Constant density No mass generation Solution : Conservation of mass gives: dt dM m m m CV gen out in = + - simplifications (no outflow; no generation) give: dt dM m CV in = Incorporate variables from problem: dt dh D h D dt d u d in 4 4 4 2 2 2 π = = Simplifying: in u D d dt dh 2 2 = Integrate from h/2 to h: ( ) full in in t u D d t t u D d h h 2 2 0 2 2 2 = - = - Solve for t full : m h s s d u D h t in full 5 2 7500 005 . 0 * 4 1 2 5 . 1 2 2 2 2 2
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

HW_4_Soln - ME 309 Fall 2008 Section 2(Merkle Homework 4...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online