Homework Answers
221. Velocity profiles are measured at the upstream end (surface 1) and at the downstream end...
221. Velocity profiles are measured at the upstream end (surface 1) and at the downstream end (surface 2) of a rectangular control volume, as shown in Fig. P2.21. If the flow is incompress- ible, two dimensional, and steady, what is the drag coefficient for the airfoil? The vertical di- mension H is 0.025c. The pressure is poo (a constant) over the entire surface of the control volume. (This is an extension of Problem 2.9.) 3)-r u=U, H 0.02501 Figure P2.21
1Hint: Use the theorem from class that any linearly independent list of vectors is contained in...
1Hint: Use the theorem from class that any linearly independent
list of vectors is contained in a basis
2Hint: Remember that we prove the equality of sets X = Y by
showing X ⊂ Y and Y ⊂ X.
(2 points each for (a),(b),(d)) In this problem, we will prove the following di- mension formula. Theorem. If H and H' are subspaces of a finite-dimensional vector space V, then dim(H+H') = dim(H)+dim(H') - dim(H nH'). (a) Suppose {u1;...; up} is...
is means that Δυ The dimensions o a quantity are not changed by addition or subtraction...
is means that Δυ The dimensions o a quantity are not changed by addition or subtraction o another quantity with the same d mens ons subtracting two speeds, has the same dimensions as speed. h ch mes rom It does not make physical sense to add or subtract two quanitites that have different dimensions, like length plus time. You can add quantities that have different units, like miles per hour and kilometers per hour, as long as you convert both...
8. Refer to the axial loading problem 3 above. In that problem you were asked to...
8. Refer to the axial loading problem 3 above. In that problem you were asked to calculate normal and shear stress components on a given plane (45° CCW as shown in that figure). Considering it as 2D plane stress problem draw a Mohr's circle and determine the normal and shear stress components on the given plane from the Mohr's circle this time. Calculate the quantities considering the geometry (which means you don't need to draw the Mohr's circle in scale...
10. Camider the ring of plynicanials z,Ir, and let/ denote the elmmont r4 + 2a +...
10. Camider the ring of plynicanials z,Ir, and let/ denote the elmmont r4 + 2a + 1 a) (5 points) Show that the quotient rga)/ () is a field. b) (5 points) Let a denote the coset z()Regarding F as a vector space over Z2, find a basis for F coasisting of powers of a c) (5 poluts) How nuany elements dors F have? Justify your answer. d) (5 points) Compute the product afas t a) i.e. expand this product...
82.6 642 6.40 - 57 5.4 R0.8 MAX 28.6 035 28.4 #51 3 45 ф100 R3 #8.5 M10 X 1.5-6H 45 4X 10.5 NOTE:...
82.6 642 6.40 - 57 5.4 R0.8 MAX 28.6 035 28.4 #51 3 45 ф100 R3 #8.5 M10 X 1.5-6H 45 4X 10.5 NOTE: ALL DIMS IN mm ーAX 90. GRAY IRON FIN. DIMS i02 UNFİN, DIMS 최 ANGLE ±0° 30' FLANGED HUB 31A059 2 Refer to drawing 31A059 to answer the following questions. the units of measurement in (a) inches, (b) millimeters, or (c) centimeters? 2. Is the section view a (a) half-section or a (b) full section? what...
221. Velocity profiles are measured at the upstream end (surface 1) and at the downstream end (surface 2) of a rectangular control volume, as shown in Fig. P2.21. If the flow is incompress- ible, two dimensional, and steady, what is the drag coefficient for the airfoil? The vertical di- mension H is 0.025c. The pressure is poo (a constant) over the entire surface of the control volume. (This is an extension of Problem 2.9.) 3)-r u=U, H 0.02501 Figure P2.21
1Hint: Use the theorem from class that any linearly independent
list of vectors is contained in a basis
2Hint: Remember that we prove the equality of sets X = Y by
showing X ⊂ Y and Y ⊂ X.
(2 points each for (a),(b),(d)) In this problem, we will prove the following di- mension formula. Theorem. If H and H' are subspaces of a finite-dimensional vector space V, then dim(H+H') = dim(H)+dim(H') - dim(H nH'). (a) Suppose {u1;...; up} is...
is means that Δυ The dimensions o a quantity are not changed by addition or subtraction o another quantity with the same d mens ons subtracting two speeds, has the same dimensions as speed. h ch mes rom It does not make physical sense to add or subtract two quanitites that have different dimensions, like length plus time. You can add quantities that have different units, like miles per hour and kilometers per hour, as long as you convert both...
8. Refer to the axial loading problem 3 above. In that problem you were asked to calculate normal and shear stress components on a given plane (45° CCW as shown in that figure). Considering it as 2D plane stress problem draw a Mohr's circle and determine the normal and shear stress components on the given plane from the Mohr's circle this time. Calculate the quantities considering the geometry (which means you don't need to draw the Mohr's circle in scale...
10. Camider the ring of plynicanials z,Ir, and let/ denote the elmmont r4 + 2a + 1 a) (5 points) Show that the quotient rga)/ () is a field. b) (5 points) Let a denote the coset z()Regarding F as a vector space over Z2, find a basis for F coasisting of powers of a c) (5 poluts) How nuany elements dors F have? Justify your answer. d) (5 points) Compute the product afas t a) i.e. expand this product...
82.6 642 6.40 - 57 5.4 R0.8 MAX 28.6 035 28.4 #51 3 45 ф100 R3 #8.5 M10 X 1.5-6H 45 4X 10.5 NOTE: ALL DIMS IN mm ーAX 90. GRAY IRON FIN. DIMS i02 UNFİN, DIMS 최 ANGLE ±0° 30' FLANGED HUB 31A059 2 Refer to drawing 31A059 to answer the following questions. the units of measurement in (a) inches, (b) millimeters, or (c) centimeters? 2. Is the section view a (a) half-section or a (b) full section? what...
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