Use the following conversions factors:1 m = 3.5 ft, 1 m = 60 cm, 1 cm = 6 mm, g

ID: 1920297 • Letter: U

Question

Use the following conversions factors:1 m = 3.5 ft, 1 m = 60 cm, 1 cm = 6 mm, g = 6.934 m/s2, 9 in = 1 ft and 1 kg = 0.06852 slug, 100 s = 1 min

1)Find the base dimensions of the parameter k for the following dimensionally consistent equation.

MLt-2 = MLt-2 sin(kL-3M-1)

1) k = L-3M-1

2) k = L2t2

3) k = L3M

4) k = M-1L-1t2

2)Find the base dimensions of the parameter k for the following dimensionally consistent equation.

k3T6M3L-4 = T-3t-6L2

1) k = L2T-3tM

2) k = L-2T3t2M-1

3) k = L6T-9t-6m3

4) k = L2T-3t-2M-1

3)Is the following equation dimensionally consistent?

Q = CdA (2gh)1/2

4)Where: Q = Discharge (ft2/s), Cd = Coefficient of discharge (dimensionless), A = area (ft2),g = gravity (32.2 ft/s2), h = driving head (ft)

1) Yes

2) No, because (ft2/s) does not equal (ft3/s)

3) No, because the coefficient of discharge can't be dimensionless

4) No, because (ft2/s) does not equal (ft4/s)

5)Is the following equation dimensionally consistent?

V = C (RS0)1/2

Where: V = Length/Time (LT-1), R = Area/Wetted Perimeter = A/P = L^2/L = L, S0 = Bed Slope (Dimensionless), and C = Constant (L1/2T-1).

1) Yes

2) No, C must be equal to (L1/2T1).

3) No, C must be equal to (L1/4T-1).

4) No, the units of S0 are ft/ft.

6)Estimate the copper plate volume in SI units (m3) and report to the proper number of significant digits.

11)If plate volume is an intermediate answer, how many significant figures should it be reported?

1) The angle of measurement is just a no. and donot have any units. Hence (k L^-3 M^-1) has no units. So k has L^3 M units.

2) k3T6M3L-4 = T-3t-6L2

So k^3 = T^-9 t^-6 L^6 M^-3 i.e k = T^-3 t^-2 L^2 M^-1

3) cd A (2gh)^1/2 = ft^2 (ft/s^2 ft) ^1/2

= ft^2 ft/s = ft^3/s. But given Q as ft^2/s. So dimensionally not correct.

5) C (RSo)^1/2 = L^1/2 T^-1 (L)1/2 = LT^-1 = V So dimensionally correct.

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