Problem 06 - Bernoulli's Energy Theorem

Problem 6
As shown in Figure 4-03, the smaller pipe is cut off a short distance past the reducer so that the jet springs free into the air. Compute the pressure at 1 if Q = 5 cfs of water. D1 = 12 inches and D2 = 4 inches. Assume that the jet has the diameter D2, that the pressure in the jet is atmospheric and that the loss of head from point 1 to point 2 is 5 ft of water.



Problem 01 - Bernoulli's Energy Theorem

Problem 1
The water surface shown in Figure 4-01 is 6 m above the datum. The pipe is 150 mm in diameter and the total loss of head between point (1) in the water surface and point (5) in the jet is 3 m. Determine the velocity of flow in the pipe and the discharge Q.



01 How to calculate the discharge and the velocity of flow

Problem 1
Compute the discharge of water through 75 mm pipe if the mean velocity is 2.5 m/sec.

Problem 2
The discharge of air through a 600-mm pipe is 4 m3/sec. Compute the mean velocity in m/sec.

Problem 3
A pipe line consists of successive lengths of 380-mm, 300-mm, and 250-mm pipe. With a continuous flow through the line of 250 Lit/sec of water, compute the mean velocity in each size of pipe.

Discharge or Flow Rate

Discharge (also called flow rate)
The amount of fluid passing a section of a stream in unit time is called the discharge. If v is the mean velocity and A is the cross sectional area, the discharge Q is defined by Q = Av which is known as volume flow rate. Discharge is also expressed as mass flow rate and weight flow rate.

Volume flow rate, $Q = Av$

Mass flow rate, $M = \rho Q$

Weight flow rate, $W = \gamma Q$




Time Rates | Applications

Time Rates
If a quantity x is a function of time t, the time rate of change of x is given by dx/dt.

When two or more quantities, all functions of t, are related by an equation, the relation between their rates of change may be obtained by differentiating both sides of the equation with respect to t.


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