The volume of microbial culture is observed to increase according to the formula
V(m^3)=e^t
where t is time in seconds
a,calculate the expression for V(in^3) in terms of t(minute)
b,

Answers

Answer 1

The expression of V(m³)=e^(t(s)) to make V in in³ and t in minutes is;

V(in³) = (¹/₆₁₀₂₄)a[tex]e^{\frac{1}{60}bt(h)[/tex]

We are given that;

Volume of microbial culture is observed to increase according to the formula;

V = e^(t)

where;

t is in seconds

V is in m³

We want to now express V in in³ and t in minutes.

Now, from conversions;

1 m³ = 61024 in³

Also; 1 second = 1/60 minutes

according to formula for exponential decay, we know that;

V = ae^(bt)

Thus, we have;

61024V = ae^(¹/₆₀b(t(h))

V(in³) = (¹/₆₁₀₂₄)a[tex]e^{\frac{1}{60}bt(h)[/tex]

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A pump of a water distribution system at 25°C is powered by a 15 kW electric motor whose efficiency is 90 percent. The water flow rate through the pump is 50 L/s. The diameters of the inlet and outlet pipes are both 5 cm and the elevation difference across the pump is negligible. If the absolute pressures at the inlet and outlet of the pump are measured as 100 kPa and 300 kPa, respectively, determine the friction loss in the system.

Answers

The friction loss in the system is 3.480 kilowatts.

Procedure - Friction loss through a pumpPump model

Let suppose that the pump within a distribution system is an open system at steady state, whose mass and energy balances are shown below:

Mass balance

[tex]\dot m_{in}-\dot m_{out} = 0[/tex] (1)

[tex]\dot m_{in} = \frac{\dot V_{in}}{\nu_{in}}[/tex] (2)

[tex]\dot m_{out} = \frac{\dot V_{out}}{\nu_{out}}[/tex] (3)

Energy balance

[tex]\eta \cdot \dot W_{el} + \dot m_{in}\cdot (h_{in}-h_{out}) - \dot W_{f} = 0[/tex] (4)

Where:

[tex]\dot m_{in}[/tex] - Inlet mass flow, in kilograms per second.[tex]\dot m_{out}[/tex] - Outlet mass flow, in kilograms per second. [tex]\dot V_{in}[/tex] - Inlet volume flow, in cubic meters per second. [tex]\dot V_{out}[/tex] - Outlet volume flow, in cubic meters per second. [tex]\nu_{in}[/tex] - Inlet specific volume, in cubic meters per kilogram.[tex]\nu_{out}[/tex] - Outlet specific volume, in cubic meters per kilogram.[tex]\eta[/tex] - Pump efficiency, no unit.[tex]\dot W_{el}[/tex] - Electric motor power, in kilowatts.[tex]h_{in}[/tex] - Inlet specific enthalpy, in kilojoules per kilogram.[tex]h_{out}[/tex] - Outlet specific enthalpy, in kilojoules per kilogram. [tex]\dot W[/tex] - Work losses due to friction, in kilowatts.

Data from steam tables

From steam tables we get the following water properties at inlet and outlet:

Inlet

[tex]p = 100\,kPa[/tex], [tex]T = 25\,^{\circ}C[/tex], [tex]\nu = 0.001003\,\frac{kJ}{kg}[/tex], [tex]h = 104.927\,\frac{kJ}{kg}[/tex], Subcooled liquid

Outlet

[tex]p = 300\,kPa[/tex], [tex]T = 25\,^{\circ}C[/tex], [tex]\nu = 0.001003\,\frac{kJ}{kg}[/tex], [tex]h = 105.128\,\frac{kJ}{kg}[/tex], Subcooled liquid

Calculation of the friction loss in the system

If we know that [tex]\dot V_{in} = 0.05\,\frac{m^{3}}{s}[/tex], [tex]\nu_{in} = 0.001003\,\frac{m^{3}}{kg}[/tex], [tex]h_{in} = 104.927\,\frac{kJ}{kg}[/tex], [tex]h_{out} = 105.128\,\frac{kJ}{kg}[/tex], [tex]\eta = 0.90[/tex] and [tex]\dot W_{el} = 15\,kW[/tex], then the friction loss in the system is:

[tex]\dot W_{f} = \frac{\dot V_{in}}{\nu_{in}}\cdot (h_{in} - h_{out}) + \eta \cdot \dot W_{el}[/tex]

[tex]\dot W_{f} = \left(\frac{0.05\,\frac{m^{3}}{s} }{0.001003\,\frac{m^{3}}{kg} } \right)\cdot \left(104.927\,\frac{kJ}{kg}-105.128\,\frac{kJ}{kg}\right) + (0.90)\cdot (15\,kW)[/tex]

[tex]\dot W_{f} = 3.480\,kW[/tex]

The friction loss in the system is 3.480 kilowatts. [tex]\blacksquare[/tex]

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The separation and purification process is used for DEVELOPING VACCINES. The development of vaccines must follow strict guidelines.

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Robert Hooke contributed a full description of living cells to the field of bioengineering

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ANSWER :

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313 + 12 = 325

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B. To accurately measure spark advance, use a timing light that incorporates an

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A student borrows $60,000 for business school at 6.5% stated annual interest with equal monthly payments over 10 years. Consider this as a loan with no payments or interest during school so that the problem structure is equivalent to a standard loan received one period before the first payment. How much is the monthly payment?

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